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27 relations: Aleksandr Lyapunov, Attractor, Chaos theory, Dissipation, Dynamical system, Eigenvalues and eigenvectors, Floquet theory, Fractal dimension, GNU Free Documentation License, Gram–Schmidt process, Information dimension, Jacobian matrix and determinant, Kaplan–Yorke conjecture, Liouville's theorem (Hamiltonian), Lyapunov stability, Lyapunov time, Lyapunov vector, Mathematics, Measure-preserving dynamical system, Multiplicative inverse, Oseledets theorem, Phase space, Predictability, Recurrence quantification analysis, Synchronization of chaos, Tisean, Trajectory.
Aleksandr Lyapunov
Aleksandr Mikhailovich Lyapunov (Алекса́ндр Миха́йлович Ляпуно́в,; – November 3, 1918) was a Russian mathematician, mechanician and physicist.
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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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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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Dissipation
Dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems.
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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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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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Floquet theory
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form with \displaystyle A(t) a piecewise continuous periodic function with period T and defines the state of the stability of solutions.
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Fractal dimension
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured.
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GNU Free Documentation License
The GNU Free Documentation License (GNU FDL or simply GFDL) is a copyleft license for free documentation, designed by the Free Software Foundation (FSF) for the GNU Project.
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Gram–Schmidt process
In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inner product.
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Information dimension
In information theory, information dimension is an information measure for random vectors in Euclidean space, based on the normalized entropy of finely quantized versions of the random vectors.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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Kaplan–Yorke conjecture
In applied mathematics, the Kaplan–Yorke conjecture concerns the dimension of an attractor, using Lyapunov exponents.
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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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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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Lyapunov time
In mathematics, the Lyapunov time is the characteristic timescale on which a dynamical system is chaotic.
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Lyapunov vector
In applied mathematics and dynamical system theory, Lyapunov vectors, named after Aleksandr Lyapunov, describe characteristic expanding and contracting directions of a dynamical system.
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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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Measure-preserving dynamical system
In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular.
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Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
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Oseledets theorem
In mathematics, the multiplicative ergodic theorem, or Oseledets theorem provides the theoretical background for computation of Lyapunov exponents of a nonlinear dynamical system.
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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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Predictability
Predictability is the degree to which a correct prediction or forecast of a system's state can be made either qualitatively or quantitatively.
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Recurrence quantification analysis
Recurrence quantification analysis (RQA) is a method of nonlinear data analysis (cf. chaos theory) for the investigation of dynamical systems.
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Synchronization of chaos
Synchronization of chaos is a phenomenon that may occur when two, or more, dissipative chaotic systems are coupled.
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Tisean
TISEAN (acronym for Time Series Analysis) is a software package for the analysis of time series with methods based on the theory of nonlinear dynamical systems.
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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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References
[1] https://en.wikipedia.org/wiki/Lyapunov_exponent
