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Lyapunov exponent

In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the exponential rate of separation of infinitesimally close trajectories. Quantitatively, two trajectories in phase space with initial separation vector δ 0 {\displaystyle {\boldsymbol {\delta }}_{0}} diverge (provided that the…

Measurement, Software & Significance of the Lyapunov spectrum

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Overview

Definition of the maximal Lyapunov exponent

Definition of the Lyapunov spectrum

Lyapunov exponent for time-varying linearization

Basic properties

Significance of the Lyapunov spectrum

Numerical calculation

Local Lyapunov exponent

Conditional Lyapunov exponent

Software

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Lyapunov exponent

Nodes59
Edges58
Triples158
Avg. degree1.97
Density0.033898
Components1

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Lyapunov exponent

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related to Further reading · 69
Lyapunov exponent → Archived, Artuso, Attractor Dimension Estimates, Aurell, Bibcode, Bifurcation, Boffetta, Cham, Chaos, Characterizing Dynamics, Chaté, Classical, Computation, Computing Lyapunov, Copenhagen, Covariant Lyapunov Vectors, Crisanti, Cvitanović, Danca, Dynamical Systems
related to Software · 26
Lyapunov exponent → Access, Alternatively, Archived, Both, Chaotic, Fortran, Hegger, Kantz, Linux/Unix, Lyap, LyapOde, Lyapunov, March, Microsoft Excel, Nonlinear Time Series Analysis, Ronald Joe Record's, Schreiber, Scientio's ChaosKit, Silverlight, The
related to Significance of the Lyapunov spectrum · 15
Lyapunov exponent → Along, For, Hausdorff, In, Kaplan, Kolmogorov, KY, Lyapunov, Lyapunov-like, Moreover, Pesin's, Sinai, The, The Lyapunov, Yorke
related to Numerical calculation · 12
Lyapunov exponent → An, Currently, Generally, Gram, Hénon, Lorenz, Lyapunov, Miller, One, Schmidt, Source, The Lyapunov
related to Definition of the Lyapunov spectrum · 10
Lyapunov exponent → For, For Hamiltonian, However, Jacobian, JY, Lambda, Lyapunov, Oseledets, The, The Lyapunov
has effect · 7
Lyapunov exponent → Also, Furthermore, In, Lyapunov, Perron, Perron's, The
related to Local Lyapunov exponent · 7
Lyapunov exponent → J0, Jacobian, Local, Lyapunov, These, This, Whereas
related to Lyapunov exponent for time-varying linearization · 5
Lyapunov exponent → Later, Lyapunov, Perron, The, To
related to Basic properties · 3
Lyapunov exponent → If, Lyapunov, Thus
related to Definition of the maximal Lyapunov exponent · 2
Lyapunov exponent → Lyapunov, The

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lyapunov exponents system exponent displaystyle time phase space initial spectrum dynamical attractor bibcode doi 10 approximation lambda original rate largest

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SubjectPredicateObjectConfidenceSrc
Lyapunov exponenthas effectIn0.60section
Lyapunov exponenthas effectPerron0.60section
Lyapunov exponenthas effectLyapunov0.60section
Lyapunov exponenthas effectFurthermore0.60section
Lyapunov exponenthas effectAlso0.60section
Lyapunov exponenthas effectThe0.60section
Lyapunov exponenthas effectPerron's0.60section
Lyapunov exponentrelated to Basic propertiesIf0.60section
Lyapunov exponentrelated to Basic propertiesThus0.60section
Lyapunov exponentrelated to Basic propertiesLyapunov0.60section
Lyapunov exponentrelated to Definition of the Lyapunov spectrumFor0.60section
Lyapunov exponentrelated to Definition of the Lyapunov spectrumLyapunov0.60section

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