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141 relations: Affine transformation, Aleksandr Lyapunov, American Mathematical Society, Anosov diffeomorphism, Arnold tongue, Arnold's cat map, Attractor, Baker's map, Banach space, Behavioral modeling, Bernard Koopman, Bifurcation diagram, Bifurcation theory, Bouncing ball, Chaos theory, Chaos: Making a New Science, Classical mechanics, Complex dynamics, Complex quadratic polynomial, Computer, Coordinate system, David Ruelle, Deterministic system, Diffeomorphism, Differential equation, Digital image processing, Double pendulum, Dyadic transformation, Dynamical billiards, Dynamical system (definition), Dynamical systems theory, Edge of chaos, Eigenvalues and eigenvectors, Equivalence relation, Ergodic hypothesis, Ergodic theory, Ernst Zermelo, ETH Zurich, Feedback passivation, Fixed point (mathematics), Florin Diacu, Flow (mathematics), Fluid dynamics, Function (mathematics), Functional analysis, George David Birkhoff, Gerald Teschl, Hamiltonian mechanics, Hartman–Grobman theorem, Hénon map, ..., Henri Poincaré, Horseshoe map, Hyperbolic equilibrium point, Infinite compositions of analytic functions, Irrational rotation, Iterated function, Jacob Palis, James A. Yorke, James Gleick, Jerrold E. Marsden, Kaplan–Yorke map, Kolmogorov–Arnold–Moser theorem, Linear dynamical system, Liouville's theorem (Hamiltonian), List of chaotic maps, List of dynamical systems and differential equations topics, List of people in systems and control, Logistic map, Lorenz system, Ludwig Boltzmann, Lyapunov stability, Manifold, Mathematical model, Mathematics, Matrix difference equation, Matrix exponential, Measurable function, Measure (mathematics), Measure space, Meteorology, Morris Hirsch, Multidimensional system, Oleksandr Mykolayovych Sharkovsky, Orbit (dynamics), Ordinary differential equation, Oscillation, Outer billiard, Partial differential equation, Pendulum, Period-doubling bifurcation, Periodic point, Phase space, Philip Holmes, Physics, Piecewise linear function, Poincaré map, Poincaré recurrence theorem, Poincaré–Bendixson theorem, Poincaré–Birkhoff theorem, Point (geometry), Population dynamics, Principle of maximum caliber, Providence, Rhode Island, Ralph Abraham (mathematician), Rössler attractor, Real line, Real number, Recurrence relation, Robert L. Devaney, Scholarpedia, Self-assembly, Set (mathematics), Sharkovskii's theorem, Sigma-algebra, Singularity (mathematics), State space, State-space representation, Statistical mechanics, Steady state, Stephen Smale, Steven Strogatz, Stochastic process, Structural stability, Superposition principle, Swinging Atwood's machine, System dynamics, Systems theory, Tangent space, Tent map, Three-body problem, Time, Time-scale calculus, Torus, Trajectory, Transfer operator, Tuple, Turbulence, Vector field, Vector space, Vladimir Arnold, Welington de Melo. Expand index (91 more) »
Affine transformation
In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.
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Aleksandr Lyapunov
Aleksandr Mikhailovich Lyapunov (Алекса́ндр Миха́йлович Ляпуно́в,; – November 3, 1918) was a Russian mathematician, mechanician and physicist.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Anosov diffeomorphism
In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of "expansion" and "contraction".
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Arnold tongue
In mathematics, particularly in dynamical systems theory, an Arnold tongue is a phase-locked or mode-locked region in a driven (kicked) weakly-coupled harmonic oscillator.
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Arnold's cat map
In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name.
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Attractor
In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system.
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Baker's map
In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Behavioral modeling
The behavioral approach to systems theory and control theory was initiated in the late-1970s by J. C. Willems as a result of resolving inconsistencies present in classical approaches based on state-space, transfer function, and convolution representations.
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Bernard Koopman
Bernard Osgood Koopman (1900 – August 18, 1981) was a French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research.
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Bifurcation diagram
In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system.
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Bifurcation theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.
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Bouncing ball
The physics of a bouncing ball concerns the physical behaviour of bouncing balls, particularly its motion before, during, and after impact against the surface of another body.
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Chaos theory
Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions.
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Chaos: Making a New Science
Chaos: Making a New Science is a debut non-fiction book by James Gleick that initially introduced the principles and early development of the chaos theory to the public.
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Classical mechanics
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.
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Complex dynamics
Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces.
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Complex quadratic polynomial
A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers.
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Computer
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
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Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
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David Ruelle
David Pierre Ruelle (born 20 August 1935) is a Belgian-French mathematical physicist.
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Deterministic system
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system.
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Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Digital image processing
In computer science, Digital image processing is the use of computer algorithms to perform image processing on digital images.
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Double pendulum
In physics and mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions.
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Dyadic transformation
The dyadic transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation) produced by the rule Equivalently, the dyadic transformation can also be defined as the iterated function map of the piecewise linear function The name bit shift map arises because, if the value of an iterate is written in binary notation, the next iterate is obtained by shifting the binary point one bit to the right, and if the bit to the left of the new binary point is a "one", replacing it with a zero.
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Dynamical billiards
A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary.
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Dynamical system (definition)
The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space.
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Dynamical systems theory
Dynamical systems theory is an area of mathematics used to describe the behavior of the complex dynamical systems, usually by employing differential equations or difference equations.
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Edge of chaos
The term edge of chaos is used to denote a transition space between order and disorder that is hypothesized to exist within a wide variety of systems.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Ergodic hypothesis
In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are equiprobable over a long period of time.
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Ergodic theory
Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems.
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Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo (27 July 1871 – 21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics.
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ETH Zurich
ETH Zurich (Swiss Federal Institute of Technology in Zurich; Eidgenössische Technische Hochschule Zürich) is a science, technology, engineering and mathematics STEM university in the city of Zürich, Switzerland.
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Feedback passivation
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Fixed point (mathematics)
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.
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Florin Diacu
Florin Diacu (April 24, 1959 – February 13, 2018) was a Romanian Canadian mathematician and author.
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Flow (mathematics)
In mathematics, a flow formalizes the idea of the motion of particles in a fluid.
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Fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
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George David Birkhoff
George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem.
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Gerald Teschl
Gerald Teschl (born May 12, 1970 in Graz) is an Austrian mathematical physicist and professor of mathematics.
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Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
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Hartman–Grobman theorem
In mathematics, in the study of dynamical systems, the Hartman–Grobman theorem or linearization theorem is a theorem about the local behavior of dynamical systems in the neighbourhood of a hyperbolic equilibrium point.
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Hénon map
The Hénon map is a discrete-time dynamical system.
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Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
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Horseshoe map
In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself.
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Hyperbolic equilibrium point
In the study of dynamical systems, a hyperbolic equilibrium point or hyperbolic fixed point is a fixed point that does not have any center manifolds.
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Infinite compositions of analytic functions
In mathematics, infinite compositions of analytic functions (ICAF) offer alternative formulations of analytic continued fractions, series, products and other infinite expansions, and the theory evolving from such compositions may shed light on the convergence/divergence of these expansions.
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Irrational rotation
In the mathematical theory of dynamical systems, an irrational rotation is a map where θ is an irrational number.
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Iterated function
In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times.
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Jacob Palis
Jacob Palis Jr. (born 15 March 1940) is a Brazilian mathematician and professor.
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James A. Yorke
James A. Yorke (born August 3, 1941) is a Distinguished University Research Professor of Mathematics and Physics and former chair of the Mathematics Department at the University of Maryland, College Park.
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James Gleick
James Gleick (born August 1, 1954) is an American author and historian of science whose work has chronicled the cultural impact of modern technology.
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Jerrold E. Marsden
Jerrold Eldon Marsden (August 17, 1942 – September 21, 2010) was a mathematician.
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Kaplan–Yorke map
The Kaplan–Yorke map is a discrete-time dynamical system.
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Kolmogorov–Arnold–Moser theorem
The Kolmogorov–Arnold–Moser theorem (KAM theorem) is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations.
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Linear dynamical system
Linear dynamical systems are dynamical systems whose evaluation functions are linear.
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Liouville's theorem (Hamiltonian)
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics.
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List of chaotic maps
In mathematics, a chaotic map is a map (.
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List of dynamical systems and differential equations topics
This is a list of dynamical system and differential equation topics, by Wikipedia page.
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List of people in systems and control
This is an alphabetical list of people who have made significant contributions in the fields of system analysis and control theory.
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Logistic map
The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations.
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Lorenz system
The Lorenz system is a system of ordinary differential equations first studied by Edward Lorenz.
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Ludwig Boltzmann
Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion).
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Lyapunov stability
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Mathematical model
A mathematical model is a description of a system using mathematical concepts and language.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix difference equation
A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices.
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Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
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Measurable function
In mathematics and in particular measure theory, a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable, analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Measure space
A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes.
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Meteorology
Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting.
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Morris Hirsch
Morris William Hirsch (born June 28, 1933) is an American mathematician, formerly at the University of California, Berkeley.
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Multidimensional system
In mathematical systems theory, a multidimensional system or m-D system is a system in which not only one dependent variable exists (like time), but there are several independent variables.
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Oleksandr Mykolayovych Sharkovsky
Oleksandr Mykolayovych Sharkovsky (also Sharkovskii) (Олекса́ндр Миколайович Шарко́вський) (born December 7, 1936) is a prominent Ukrainian mathematician most famous for developing Sharkovsky's theorem on the periods of discrete dynamical systems in 1964.
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Orbit (dynamics)
In mathematics, in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states.
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Outer billiard
Outer billiards is a dynamical system based on a convex shape in the plane.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely.
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Period-doubling bifurcation
In mathematics, a period doubling bifurcation in a discrete dynamical system is a bifurcation in which a slight change in a parameter value in the system's equations leads to the system switching to a new behavior with twice the period of the original system.
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Periodic point
In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time.
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Phase space
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space.
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Philip Holmes
Philip John Holmes (born May 24, 1945) is the Eugene Higgins Professor of Mechanical and Aerospace Engineering at Princeton University.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Piecewise linear function
In mathematics, a piecewise linear function is a real-valued function defined on the real numbers or a segment thereof, whose graph is composed of straight-line sections.
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Poincaré map
In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.
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Poincaré recurrence theorem
In physics, the Poincaré recurrence theorem states that certain systems will, after a sufficiently long but finite time, return to a state very close to, if not exactly the same as, the initial state.
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Poincaré–Bendixson theorem
In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.
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Poincaré–Birkhoff theorem
In symplectic topology and dynamical systems, Poincaré–Birkhoff theorem (also known as Poincaré–Birkhoff fixed point theorem and Poincaré's last geometric theorem) states that every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points.
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Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
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Population dynamics
Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them (such as birth and death rates, and by immigration and emigration).
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Principle of maximum caliber
The principle of maximum caliber (MaxCal) or maximum path entropy principle, suggested by E. T. Jaynes, can be considered as a generalization of the principle of maximum entropy.
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Providence, Rhode Island
Providence is the capital and most populous city of the U.S. state of Rhode Island and is one of the oldest cities in the United States.
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Ralph Abraham (mathematician)
Ralph H. Abraham (born July 4, 1936) is an American mathematician.
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Rössler attractor
The Rössler attractor is the attractor for the Rössler system, a system of three non-linear ordinary differential equations originally studied by Otto Rössler.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
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Robert L. Devaney
Robert Luke Devaney (born 1948) is an American mathematician, the Feld Family Professor of Teaching Excellence at Boston University.
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Scholarpedia
Scholarpedia is an English-language online wiki-based encyclopedia with features commonly associated with open-access online academic journals, which aims to have quality content.
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Self-assembly
Self-assembly is a process in which a disordered system of pre-existing components forms an organized structure or pattern as a consequence of specific, local interactions among the components themselves, without external direction.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Sharkovskii's theorem
In mathematics, Sharkovskii's theorem, named after Oleksandr Mykolaiovych Sharkovskii who published it in 1964, is a result about discrete dynamical systems.
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Sigma-algebra
In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections.
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Singularity (mathematics)
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.
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State space
In the theory of discrete dynamical systems, a state space is the set of all possible configurations of a system.
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State-space representation
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations.
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Statistical mechanics
Statistical mechanics is one of the pillars of modern physics.
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Steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time.
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Stephen Smale
Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan.
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Steven Strogatz
Steven Henry Strogatz (born August 13, 1959) is an American mathematician and the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University.
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Stochastic process
--> In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.
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Structural stability
In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations (to be exact ''C''1-small perturbations).
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Superposition principle
In physics and systems theory, the superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually.
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Swinging Atwood's machine
The swinging Atwood's machine (SAM) is a mechanism that resembles a simple Atwood's machine except that one of the masses is allowed to swing in a two-dimensional plane, producing a dynamical system that is chaotic for some system parameters and initial conditions.
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System dynamics
System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays.
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Systems theory
Systems theory is the interdisciplinary study of systems.
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Tangent space
In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.
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Tent map
In mathematics, the tent map with parameter μ is the real-valued function fμ defined by the name being due to the tent-like shape of the graph of fμ.
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Three-body problem
In physics and classical mechanics, the three-body problem is the problem of taking an initial set of data that specifies the positions, masses, and velocities of three bodies for some particular point in time and then determining the motions of the three bodies, in accordance with Newton's laws of motion and of universal gravitation, which are the laws of classical mechanics.
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Time
Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.
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Time-scale calculus
In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid discrete–continuous dynamical systems.
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Torus
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
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Trajectory
A trajectory or flight path is the path that a massive object in motion follows through space as a function of time.
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Transfer operator
In mathematics, the transfer operator encodes information about an iterated map and is frequently used to study the behavior of dynamical systems, statistical mechanics, quantum chaos and fractals.
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Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements.
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Turbulence
In fluid dynamics, turbulence or turbulent flow is any pattern of fluid motion characterized by chaotic changes in pressure and flow velocity.
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Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Vladimir Arnold
Vladimir Igorevich Arnold (alternative spelling Arnol'd, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician.
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Welington de Melo
Welington Celso de Melo (17 November 1946 – 21 December 2016) was a Brazilian mathematician.
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Continuous dynamical system, Dynamic System, Dynamic system, Dynamic systems, Dynamical, Dynamical Systems, Dynamical systems, Mathematical dynamics, Non-integrable system, Non-linear dynamical system, Non-linear dynamics, Nonlinear dynamic system, Nonlinear dynamical system, Nonlinear dynamical systems.
References
[1] https://en.wikipedia.org/wiki/Dynamical_system
