Building Thermodynamics for Non-uniformly Hyperbolic Maps

Vaughn Climenhaga, Yakov B. Pesin

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We briefly survey the theory of thermodynamic formalism for uniformly hyperbolic systems, and then describe several recent approaches to the problem of extending this theory to non-uniform hyperbolicity. The first of these approaches involves Markov models such as Young towers, countable-state Markov shifts, and inducing schemes. The other two are less fully developed but have seen significant progress in the last few years: these involve coarse-graining techniques (expansivity and specification) and geometric arguments involving push-forward of densities on admissible manifolds.

Original languageEnglish (US)
Pages (from-to)37-82
Number of pages46
JournalArnold Mathematical Journal
Volume3
Issue number1
DOIs
StatePublished - Apr 1 2017

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Thermodynamics
Nonuniform Hyperbolicity
Thermodynamic Formalism
Coarse-graining
Hyperbolic Systems
Markov Model
Countable
Specification

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Building Thermodynamics for Non-uniformly Hyperbolic Maps. / Climenhaga, Vaughn; Pesin, Yakov B.

In: Arnold Mathematical Journal, Vol. 3, No. 1, 01.04.2017, p. 37-82.

Research output: Contribution to journalArticle

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