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110 relations: Algebra, Asymptotic analysis, Belousov–Zhabotinsky reaction, Bifurcation theory, Boundary value problem, Butterfly effect, Cantor set, Celso Grebogi, Chaos theory, Commensurability (mathematics), Complex analysis, Complex plane, Configuration space (physics), Coordinate vector, Critical point (mathematics), Curve, Cycle detection, David Ruelle, Deformation (engineering), Deformation (mechanics), Differentiable function, Differential equation, Discrete time and continuous time, Dissipative system, Dynamical system, Economics, Edward Norton Lorenz, Edward Ott, Eigenvalues and eigenvectors, Fixed point (mathematics), Floris Takens, Fractal, Friction, Geometric primitive, Geometry, Hénon map, Hidden oscillation, Homeomorphism, Horseshoe map, Hyperbolic set, Inflation, Initial condition, Integral, Intersection (set theory), Irrational number, Isolated point, Iteration, James Gleick, John Milnor, Lakes of Wada, ..., Limit cycle, Limit set, Line (geometry), Linear system, Logistic map, Lorenz system, Manifold, Mathematics, Matrix difference equation, Measure (mathematics), Metric space, Multiscroll attractor, Navier–Stokes equations, Neighbourhood (mathematics), Newton's method, Nonlinear system, Notices of the American Mathematical Society, Open set, Parabolic partial differential equation, PDF, Pendulum clock, Periodic function, Periodic point, Phase space, Physics, Plastic, Point (geometry), Quantum mechanics, Quasiperiodicity, Rössler attractor, Real number, Recurrence relation, Scalar (mathematics), Sine, Space (mathematics), Spectral density, Sphere, Square matrix, Stability theory, Stable distribution, Stable manifold, Steady state, Stephen Smale, Stiction, Strange nonchaotic attractor, Structural stability, Subset, Surface (topology), Surface roughness, System of linear equations, The Mathematical Gazette, Thermodynamics, Three-dimensional space, Topology, Toroid, Torus, Trajectory, Unemployment, Union (set theory), Van der Pol oscillator. Expand index (60 more) »
Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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Asymptotic analysis
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.
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Belousov–Zhabotinsky reaction
A Belousov–Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator.
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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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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
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Butterfly effect
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.
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Cantor set
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.
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Celso Grebogi
Celso Grebogi (born 1947) is a Brazilian theoretical physicist who works in the area of chaos theory.
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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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Commensurability (mathematics)
In mathematics, two non-zero real numbers a and b are said to be commensurable if their ratio is a rational number; otherwise a and b are called incommensurable.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
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Configuration space (physics)
In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system.
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Coordinate vector
In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers that describes the vector in terms of a particular ordered basis.
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Critical point (mathematics)
In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0.
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Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
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Cycle detection
In computer science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values.
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David Ruelle
David Pierre Ruelle (born 20 August 1935) is a Belgian-French mathematical physicist.
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Deformation (engineering)
In materials science, deformation refers to any changes in the shape or size of an object due to-.
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Deformation (mechanics)
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration.
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Differentiable function
In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Discrete time and continuous time
In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.
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Dissipative system
A dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter.
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Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
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Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
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Edward Norton Lorenz
Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician, meteorologist, and a pioneer of chaos theory.
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Edward Ott
Edward Ott is an American physicist most noted for his contributions to the development of chaos theory.
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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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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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Floris Takens
Floris Takens (November 12, 1940 – June 20, 2010) was a Dutch mathematician known for contributions to the theory of chaotic dynamical systems.
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Fractal
In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.
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Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.
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Geometric primitive
The term geometric primitive, or prim, in computer graphics and CAD systems is used in various senses, with the common meaning of the simplest (i.e. 'atomic' or irreducible) geometric objects that the system can handle (draw, store).
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Hénon map
The Hénon map is a discrete-time dynamical system.
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Hidden oscillation
An oscillation in a dynamical system can be easily localized numerically if initial conditions from its open neighborhood lead to long-run behavior that approaches the oscillation.
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Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
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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 set
In dynamical systems theory, a subset Λ of a smooth manifold M is said to have a hyperbolic structure with respect to a smooth map f if its tangent bundle may be split into two invariant subbundles, one of which is contracting and the other is expanding under f, with respect to some Riemannian metric on M. An analogous definition applies to the case of flows.
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Inflation
In economics, inflation is a sustained increase in price level of goods and services in an economy over a period of time.
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Initial condition
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
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Irrational number
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
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Isolated point
In mathematics, a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S but there exists a neighborhood of x which does not contain any other points of S. This is equivalent to saying that the singleton is an open set in the topological space S (considered as a subspace of X).
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Iteration
Iteration is the act of repeating a process, to generate a (possibly unbounded) sequence of outcomes, with the aim of approaching a desired goal, target or result.
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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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John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, K-theory and dynamical systems.
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Lakes of Wada
In mathematics, the are three disjoint connected open sets of the plane or open unit square with the counterintuitive property that they all have the same boundary.
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Limit cycle
In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity.
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Limit set
In mathematics, especially in the study of dynamical systems, a limit set is the state a dynamical system reaches after an infinite amount of time has passed, by either going forward or backwards in time.
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Line (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
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Linear system
A linear system is a mathematical model of a system based on the use of a linear operator.
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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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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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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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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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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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Multiscroll attractor
In the mathematics of dynamical systems, the double-scroll attractor (sometimes known as Chua's attractor) is a strange attractor observed from a physical electronic chaotic circuit (generally, Chua's circuit) with a single nonlinear resistor (see Chua's Diode).
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Navier–Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.
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Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
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Newton's method
In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
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Nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
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Notices of the American Mathematical Society
Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Parabolic partial differential equation
A parabolic partial differential equation is a type of partial differential equation (PDE).
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The Portable Document Format (PDF) is a file format developed in the 1990s to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.
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Pendulum clock
A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element.
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Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.
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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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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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Plastic
Plastic is material consisting of any of a wide range of synthetic or semi-synthetic organic compounds that are malleable and so can be molded into solid objects.
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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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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Quasiperiodicity
Quasiperiodicity is the property of a system that displays irregular periodicity.
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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 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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Scalar (mathematics)
A scalar is an element of a field which is used to define a vector space.
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Sine
In mathematics, the sine is a trigonometric function of an angle.
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Space (mathematics)
In mathematics, a space is a set (sometimes called a universe) with some added structure.
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Spectral density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal.
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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Square matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns.
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Stability theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions.
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Stable distribution
No description.
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Stable manifold
In mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor.
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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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Stiction
Stiction is the static friction that needs to be overcome to enable relative motion of stationary objects in contact.
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Strange nonchaotic attractor
In mathematics, a strange nonchaotic attractor (SNA) is a form of attractor, which while converging to a limit, is strange, because it is not piecewise differentiable, and also non-chaotic, in that its Lyapunov exponents are non-positive.
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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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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Surface (topology)
In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.
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Surface roughness
Surface roughness often shortened to roughness, is a component of surface texture.
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System of linear equations
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.
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The Mathematical Gazette
The Mathematical Gazette is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching.
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Thermodynamics
Thermodynamics is the branch of physics concerned with heat and temperature and their relation to energy and work.
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Three-dimensional space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Toroid
In mathematics, a toroid is a surface of revolution with a hole in the middle, like a doughnut, forming a solid body.
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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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Unemployment
Unemployment is the situation of actively looking for employment but not being currently employed.
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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Van der Pol oscillator
In dynamics, the Van der Pol oscillator is a non-conservative oscillator with non-linear damping.
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Attraction basin, Attractor basin, Attractor set, Basin of attraction, Basins of attraction, Chaotic attractor, Periodic attractor, Periodic point attractor, Point attractor, Repellor, Stable attractor, Strange attractor, Strange attractors.
References
[1] https://en.wikipedia.org/wiki/Attractor
