Path integrals in the symbol space of chaotic mappings

C. Beck, T. Tél

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 - 1995

Fingerprint

Curvilinear integral
Entropy
Non-Markovian Processes
entropy
Thermodynamic Formalism
functionals
Rényi Entropy
Transfer Operator
Symbolic Dynamics
Wiener Process
Partition Function
Stochastic Processes
stochastic processes
Random processes
Calculate
partitions
Arbitrary
Thermodynamics
formalism
operators

ASJC Scopus subject areas

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

Cite this

Path integrals in the symbol space of chaotic mappings. / Beck, C.; Tél, T.

In: Journal of Physics A: General Physics, Vol. 28, No. 7, 012, 1995, p. 1889-1907.

Research output: Contribution to journalArticle

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