Path integrals in the symbol space of chaotic mappings

C. Beck, T. Tel

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We introduce a path-integral-like partition function for chaotic mappings. This path integral is based on arbitrary non-Markovian stochastic processes generated by the symbolic dynamics of the map rather than the Wiener process. Our approach can be regarded as an extension of the thermodynamic formalism to infinitely many inverse temperatures. The concept of Renyi entropies is generalized to entropy functionals. A generalized transfer operator is introduced, which allows us to calculate the entropy functionals with high numerical precision. Several examples are worked out in detail.

Original languageEnglish
Article number012
Pages (from-to)1889-1907
Number of pages19
JournalJournal of Physics A: General Physics
Volume28
Issue number7
DOIs
Publication statusPublished - Dec 1 1995

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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