Computation of entropy and Lyapunov exponent by a shift transform

We present a novel computational method to estimate the topological entropy and Lyapunov exponent of nonlinear maps using a shift transform. Unlike the computation of periodic orbits or the symbolic dynamical approach by the Markov partition, the method presented here does not require any special te...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2015-10, Vol.25 (10), p.103110-103110
Main Authors: Matsuoka, Chihiro, Hiraide, Koichi
Format: Article
Language:English
Subjects:
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computation
ENTROPY
Liapunov exponents
LYAPUNOV METHOD
MARKOV PROCESS
Markov processes
Mathematical analysis
NONLINEAR PROBLEMS
ORBITS
PERIODICITY
TOPOLOGY
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Summary:We present a novel computational method to estimate the topological entropy and Lyapunov exponent of nonlinear maps using a shift transform. Unlike the computation of periodic orbits or the symbolic dynamical approach by the Markov partition, the method presented here does not require any special techniques in computational and mathematical fields to calculate these quantities. In spite of its simplicity, our method can accurately capture not only the chaotic region but also the non-chaotic region (window region) such that it is important physically but the (Lebesgue) measure zero and usually hard to calculate or observe. Furthermore, it is shown that the Kolmogorov-Sinai entropy of the Sinai-Ruelle-Bowen measure (the physical measure) coincides with the topological entropy.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4930956