### 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 language | English |
---|---|

Article number | 012 |

Pages (from-to) | 1889-1907 |

Number of pages | 19 |

Journal | Journal of Physics A: General Physics |

Volume | 28 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1995 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: General Physics*,

*28*(7), 1889-1907. [012]. https://doi.org/10.1088/0305-4470/28/7/012

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

Research output: Contribution to journal › Article

*Journal of Physics A: General Physics*, vol. 28, no. 7, 012, pp. 1889-1907. https://doi.org/10.1088/0305-4470/28/7/012

}

TY - JOUR

T1 - Path integrals in the symbol space of chaotic mappings

AU - Beck, C.

AU - Tél, T.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21844517909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844517909&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/28/7/012

DO - 10.1088/0305-4470/28/7/012

M3 - Article

VL - 28

SP - 1889

EP - 1907

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 7

M1 - 012

ER -