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