Piecewise linear maps, Liapunov exponents and entropy

Jonq Juang, Shih Feng Shieh

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let LA = {fA, x : x is a partition of [0, 1]} be a class of piecewise linear maps associated with a transition matrix A. In this paper, we prove that if fA, x ∈ LA, then the Liapunov exponent λ (x) of fA, x is equal to a measure theoretic entropy hmA, x of fA, x, where mA, x is a Markov measure associated with A and x. The Liapunov exponent and the entropy are computable by solving an eigenvalue problem and can be explicitly calculated when the transition matrix A is symmetric. Moreover, we also show that maxx λ (x) = maxx hmA, x = log (λ1), where λ1 is the maximal eigenvalue of A.

Original languageEnglish
Pages (from-to)358-364
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Volume338
Issue number1
DOIs
Publication statusPublished - 2008 Feb 1

Keywords

  • Entropy
  • Ergodic theory
  • Liapunov exponents
  • Piecewise linear map

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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