Building Thermodynamics for Non-uniformly Hyperbolic Maps

Vaughn Climenhaga, Yakov Pesin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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