2016, ISBN 1107030420

Web Resource

12/2017, 1st ed. 2017, ISBN 9783319712604, 273

This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic...

Lyapunov exponents | Differential equations | Dynamical Systems and Ergodic Theory | Mathematics

Lyapunov exponents | Differential equations | Dynamical Systems and Ergodic Theory | Mathematics

eBook

2007, Encyclopedia of mathematics and its applications, ISBN 0521832586, Volume 115, xiv, 513

Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account...

Lyapunov exponents | Lyapunov stability | Dynamics

Lyapunov exponents | Lyapunov stability | Dynamics

Book

Chaos, ISSN 1054-1500, 2015, Volume 25, Issue 8, p. 087407

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence...

UNSTABLE PERIODIC-ORBITS | MATHEMATICS, APPLIED | LYAPUNOV EXPONENTS | CHAOTIC SYSTEMS | TOPOLOGICAL FLUID-MECHANICS | STATISTICS | DISPERSION | ALGORITHM | LAGRANGIAN COHERENT STRUCTURES | FLOWS | PHYSICS, MATHEMATICAL | ENTROPY

UNSTABLE PERIODIC-ORBITS | MATHEMATICS, APPLIED | LYAPUNOV EXPONENTS | CHAOTIC SYSTEMS | TOPOLOGICAL FLUID-MECHANICS | STATISTICS | DISPERSION | ALGORITHM | LAGRANGIAN COHERENT STRUCTURES | FLOWS | PHYSICS, MATHEMATICAL | ENTROPY

Journal Article

2002, University lecture series, ISBN 0821829211, Volume 23., xii, 151

Book

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 11/2016, Volume 92, pp. 73 - 85

This review paper aims at answering a basic question on the sign of Lyapunov exponents. A few recent papers reported hyperchaotic system having the sign of...

Lyapunov exponents | Nature of Lyapunov exponents | Measure of hyperchaos | SYNCHRONIZATION | CHAOS | NUMBER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LIAPUNOV EXPONENTS | PHYSICS, MULTIDISCIPLINARY | SPECTRUM | PHYSICS, MATHEMATICAL | Algorithms

Lyapunov exponents | Nature of Lyapunov exponents | Measure of hyperchaos | SYNCHRONIZATION | CHAOS | NUMBER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LIAPUNOV EXPONENTS | PHYSICS, MULTIDISCIPLINARY | SPECTRUM | PHYSICS, MATHEMATICAL | Algorithms

Journal Article

2014, Cambridge studies in advanced mathematics, ISBN 9781107081734, Volume 145

"The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the...

Lyapunov exponents

Lyapunov exponents

Web Resource

International Journal of Bifurcation and Chaos, ISSN 0218-1274, 05/2018, Volume 28, Issue 5, p. 1850067

In this paper, the Benettin–Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo’s derivative and the...

Lyapunov exponents | fractional-order dynamical system | Benettin-Wolf algorithm | MULTIDISCIPLINARY SCIENCES | DIFFERENTIAL-EQUATIONS | STRANGE ATTRACTORS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DYNAMICAL-SYSTEMS | DIMENSION | TIME-SERIES | COMPUTATION | SPECTRA

Lyapunov exponents | fractional-order dynamical system | Benettin-Wolf algorithm | MULTIDISCIPLINARY SCIENCES | DIFFERENTIAL-EQUATIONS | STRANGE ATTRACTORS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DYNAMICAL-SYSTEMS | DIMENSION | TIME-SERIES | COMPUTATION | SPECTRA

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 06/2013, Volume 46, Issue 25, pp. 254002 - 29

Generic dynamical systems have 'typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system also...

INTERMITTENCY | ENERGY | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | MONTE-CARLO CALCULATION | DYNAMICAL-SYSTEMS | TRAJECTORIES | ORBITS | CHAOTIC BEHAVIOR | SOLAR-SYSTEM | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL | Lyapunov exponents | Chaos theory | Mathematical models | Trajectories | Topology | Deviation | Sampling | Dynamical systems | Breathers | Condensed Matter | Chaotic Dynamics | Nonlinear Sciences | Statistical Mechanics | Pattern Formation and Solitons | Physics

INTERMITTENCY | ENERGY | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | MONTE-CARLO CALCULATION | DYNAMICAL-SYSTEMS | TRAJECTORIES | ORBITS | CHAOTIC BEHAVIOR | SOLAR-SYSTEM | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL | Lyapunov exponents | Chaos theory | Mathematical models | Trajectories | Topology | Deviation | Sampling | Dynamical systems | Breathers | Condensed Matter | Chaotic Dynamics | Nonlinear Sciences | Statistical Mechanics | Pattern Formation and Solitons | Physics

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2005, Volume 212, Issue 3, pp. 271 - 304

This paper develops the theory and computation of Lagrangian Coherent Structures (LCS), which are defined as of Finite-Time Lyapunov Exponent (FTLE) fields....

Coherent structures | Mixing | Transport barriers | Direct and finite-time Lyapunov exponents | FIELDS | MATHEMATICS, APPLIED | HIGH-FREQUENCY RADAR | DOUBLE-GYRE | PHYSICS, MULTIDISCIPLINARY | mixing | SURFACE CURRENTS | coherent structures | INVARIANT-MANIFOLDS | PHYSICS, MATHEMATICAL | transport barriers | MEANDERING JET | TRANSPORT | PREDICTABILITY | DYNAMICAL-SYSTEMS | direct and finite-time Lyapunov exponents | POLAR VORTEX | Radar systems | Mechanical engineering | Analysis | Aerospace engineering

Coherent structures | Mixing | Transport barriers | Direct and finite-time Lyapunov exponents | FIELDS | MATHEMATICS, APPLIED | HIGH-FREQUENCY RADAR | DOUBLE-GYRE | PHYSICS, MULTIDISCIPLINARY | mixing | SURFACE CURRENTS | coherent structures | INVARIANT-MANIFOLDS | PHYSICS, MATHEMATICAL | transport barriers | MEANDERING JET | TRANSPORT | PREDICTABILITY | DYNAMICAL-SYSTEMS | direct and finite-time Lyapunov exponents | POLAR VORTEX | Radar systems | Mechanical engineering | Analysis | Aerospace engineering

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 01/2018, Volume 490, pp. 834 - 844

The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE)...

Conservative systems | Hurst exponent | Chirikov standard map | Maximal Lyapunov exponent | Machine learning | SYMPLECTIC MAPS | NUMBER | PHYSICS, MULTIDISCIPLINARY | GAMMA-RAY BURSTS | CHAOS | MOTION | TIME-SERIES | MOVING AVERAGE | SYSTEMS | COMPUTATION | GALAXIES

Conservative systems | Hurst exponent | Chirikov standard map | Maximal Lyapunov exponent | Machine learning | SYMPLECTIC MAPS | NUMBER | PHYSICS, MULTIDISCIPLINARY | GAMMA-RAY BURSTS | CHAOS | MOTION | TIME-SERIES | MOVING AVERAGE | SYSTEMS | COMPUTATION | GALAXIES

Journal Article

Systems & Control Letters, ISSN 0167-6911, 03/2018, Volume 113, pp. 78 - 85

In this paper we study the notion of estimation entropy established by Liberzon and Mitra. This quantity measures the smallest rate of information about the...

Minimal data rates | Volume-preserving systems | Lyapunov exponents | Estimation entropy | [formula omitted]-entropy | α-entropy | alpha-entropy | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABILIZATION | SYSTEMS | CHANNELS | AUTOMATION & CONTROL SYSTEMS

Minimal data rates | Volume-preserving systems | Lyapunov exponents | Estimation entropy | [formula omitted]-entropy | α-entropy | alpha-entropy | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STABILIZATION | SYSTEMS | CHANNELS | AUTOMATION & CONTROL SYSTEMS

Journal Article

IEEE Transactions on Circuits and Systems I: Regular Papers, ISSN 1549-8328, 08/2014, Volume 61, Issue 8, pp. 2380 - 2389

This paper introduces a new and unified approach for designing desirable dissipative hyperchaotic systems. Based on the anti-control principle of...

Jacobian matrices | Couplings | Chaos | closed-loop cascade-coupling | dissipative system | Lyapunov exponent | Circumferential distribution of eigenvalues | hyperchaotic system | Control systems | Eigenvalues and eigenfunctions | Mathematical model | Equations | MULTIAGENT SYSTEMS | CONSENSUS | ENGINEERING, ELECTRICAL & ELECTRONIC | ATTRACTORS | SYNCHRONIZATION | DYNAMICS | COUPLED CHUA CIRCUITS | EQUATION | STATE-FEEDBACK CONTROL | Liapunov functions | Chaos theory | Analysis | Construction | Lyapunov exponents | Dissipation | Differential equations | Eigenvalues | Mathematical models | Adjustable | Jacobians

Jacobian matrices | Couplings | Chaos | closed-loop cascade-coupling | dissipative system | Lyapunov exponent | Circumferential distribution of eigenvalues | hyperchaotic system | Control systems | Eigenvalues and eigenfunctions | Mathematical model | Equations | MULTIAGENT SYSTEMS | CONSENSUS | ENGINEERING, ELECTRICAL & ELECTRONIC | ATTRACTORS | SYNCHRONIZATION | DYNAMICS | COUPLED CHUA CIRCUITS | EQUATION | STATE-FEEDBACK CONTROL | Liapunov functions | Chaos theory | Analysis | Construction | Lyapunov exponents | Dissipation | Differential equations | Eigenvalues | Mathematical models | Adjustable | Jacobians

Journal Article

Physics Letters A, ISSN 0375-9601, 01/2014, Volume 378, Issue 1-2, pp. 34 - 42

The problem of estimating the maximum Lyapunov exponents of the motion in a multiplet of interacting nonlinear resonances is considered for the case when the...

Separatrix map | Chaotic dynamics | Standard map | Hamiltonian dynamics | Lyapunov exponents | Resonances | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | OUTER ASTEROID BELT | CHAOTIC ROTATION | PLANETARY SATELLITES | MOTION | SYSTEMS | STABLE CHAOS | SEPARATRICES | LAYER | MAP | Adiabatic flow | Maps | Control equipment | Solid state physics | Nonlinearity | Mathematical models | Standards | Physics - Chaotic Dynamics

Separatrix map | Chaotic dynamics | Standard map | Hamiltonian dynamics | Lyapunov exponents | Resonances | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | OUTER ASTEROID BELT | CHAOTIC ROTATION | PLANETARY SATELLITES | MOTION | SYSTEMS | STABLE CHAOS | SEPARATRICES | LAYER | MAP | Adiabatic flow | Maps | Control equipment | Solid state physics | Nonlinearity | Mathematical models | Standards | Physics - Chaotic Dynamics

Journal Article

Expert Systems With Applications, ISSN 0957-4174, 2005, Volume 29, Issue 3, pp. 506 - 514

There are a number of different quantitative models that can be used in a medical diagnostic decision support system including parametric methods,...

Recurrent neural networks | Electroencephalogram (EEG) signals | Levenberg–Marquardt algorithm | Chaotic signal | Lyapunov exponents | Levenberg-Marquardt algorithm | electroencephalogram (EEG) signals | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | chaotic signal | PREDICTION | ENGINEERING, ELECTRICAL & ELECTRONIC | TEMPORAL SEQUENCES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | recurrent neural networks | MULTILAYER PERCEPTRON | TIME-SERIES | SYSTEMS | Algorithms | Neural networks | Epilepsy | Analysis

Recurrent neural networks | Electroencephalogram (EEG) signals | Levenberg–Marquardt algorithm | Chaotic signal | Lyapunov exponents | Levenberg-Marquardt algorithm | electroencephalogram (EEG) signals | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | chaotic signal | PREDICTION | ENGINEERING, ELECTRICAL & ELECTRONIC | TEMPORAL SEQUENCES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | recurrent neural networks | MULTILAYER PERCEPTRON | TIME-SERIES | SYSTEMS | Algorithms | Neural networks | Epilepsy | Analysis

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 06/2013, Volume 33, Issue 3, pp. 693 - 712

We consider locally minimizing measures for conservative twist maps of the d-dimensional annulus and for Tonelli Hamiltonian flows defined on a cotangent...

MATHEMATICS | MATHEMATICS, APPLIED | CONJUGATE-POINTS | LAGRANGIAN SYSTEMS | ENTROPY | Mathematical analysis | Dynamical systems | Lower bounds | Splitting | Maps | Twisting | Lyapunov exponents | Upper bounds | Bundles | Mathematics - Dynamical Systems | Dynamical Systems | Mathematics

MATHEMATICS | MATHEMATICS, APPLIED | CONJUGATE-POINTS | LAGRANGIAN SYSTEMS | ENTROPY | Mathematical analysis | Dynamical systems | Lower bounds | Splitting | Maps | Twisting | Lyapunov exponents | Upper bounds | Bundles | Mathematics - Dynamical Systems | Dynamical Systems | Mathematics

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2019, Volume 371, Issue 9, pp. 6025 - 6046

Let K be a complete, algebraically closed, non-Archimedean valued field, and let \mathrm {\bold P}^1 denote the Berkovich projective line over K. The Lyapunov...

MATHEMATICS | EQUIDISTRIBUTION | non-Archimedean | Lyapunov exponent | DYNAMICS | lower bound | POINTS | HEIGHT | rational map | distortion

MATHEMATICS | EQUIDISTRIBUTION | non-Archimedean | Lyapunov exponent | DYNAMICS | lower bound | POINTS | HEIGHT | rational map | distortion

Journal Article

Physical Review Letters, ISSN 0031-9007, 07/2016, Volume 117, Issue 3, p. 034101

We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We...

INTERMITTENCY | CHAOTIC SYSTEMS | PHYSICS, MULTIDISCIPLINARY | EQUILIBRIUM | GROWTH | INTERFACES | DYNAMICS | DIFFUSION | MODEL | Correlation | Fluid dynamics | Lyapunov exponents | Fluctuation | Fluid flow | Breakdown | Evolution | Diffusion coefficient | Physics - Chaotic Dynamics

INTERMITTENCY | CHAOTIC SYSTEMS | PHYSICS, MULTIDISCIPLINARY | EQUILIBRIUM | GROWTH | INTERFACES | DYNAMICS | DIFFUSION | MODEL | Correlation | Fluid dynamics | Lyapunov exponents | Fluctuation | Fluid flow | Breakdown | Evolution | Diffusion coefficient | Physics - Chaotic Dynamics

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 06/2018, Volume 20, Issue 4, p. 1750027

We give a complete characterization of the existence of Lyapunov coordinate changes bringing an invertible sequence of matrices to one in block form. In other...

Lyapunov exponents | reduction | Lyapunov regularity | MATHEMATICS | MATHEMATICS, APPLIED

Lyapunov exponents | reduction | Lyapunov regularity | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 06/2013, Volume 46, Issue 25, pp. 254001 - 17

This paper reviews some basic mathematical results on Lyapunov exponents, one of the most fundamental concepts in dynamical systems. The first few sections...

DIFFEOMORPHISMS | MAPS | PHYSICS, MULTIDISCIPLINARY | DIMENSION | RANDOM TRANSFORMATIONS | SYSTEMS | ENTROPY FORMULA | STRANGE ATTRACTORS | ERGODIC-THEORY | BOWEN-RUELLE MEASURES | PHYSICS, MATHEMATICAL | METRIC ENTROPY | Maps | Nonuniform | Lyapunov exponents | Chaos theory | Dynamics | Mathematical analysis | Entropy | Dynamical systems | Invariants

DIFFEOMORPHISMS | MAPS | PHYSICS, MULTIDISCIPLINARY | DIMENSION | RANDOM TRANSFORMATIONS | SYSTEMS | ENTROPY FORMULA | STRANGE ATTRACTORS | ERGODIC-THEORY | BOWEN-RUELLE MEASURES | PHYSICS, MATHEMATICAL | METRIC ENTROPY | Maps | Nonuniform | Lyapunov exponents | Chaos theory | Dynamics | Mathematical analysis | Entropy | Dynamical systems | Invariants

Journal Article

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