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Title: 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 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.
Authors:
 [1] ;  [2]
  1. Department of Physics, Graduate School of Science and Technology, Ehime University, Matsuyama, Ehime 790-8577 (Japan)
  2. Department of Mathematics, Graduate School of Science and Technology, Ehime University, Matsuyama, Ehime 790-8577 (Japan)
Publication Date:
OSTI Identifier:
22482286
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; ENTROPY; LYAPUNOV METHOD; MAPS; MARKOV PROCESS; NONLINEAR PROBLEMS; ORBITS; PERIODICITY; TOPOLOGY