The Geometric Approach for Constructing Sinai–Ruelle–Bowen Measures

Vaughn Climenhaga; Stefano Luzzatto; Yakov Pesin

doi:10.1007/s10955-016-1608-7

The Geometric Approach for Constructing Sinai–Ruelle–Bowen Measures

Vaughn Climenhaga
, Stefano Luzzatto
, Yakov Pesin

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

An important class of ‘physically relevant’ measures for dynamical systems with hyperbolic behavior is given by Sinai–Ruelle–Bowen (SRB) measures. We survey various techniques for constructing SRB measures and studying their properties, paying special attention to the geometric ‘push-forward’ approach. After describing this approach in the uniformly hyperbolic setting, we review recent work that extends it to non-uniformly hyperbolic systems.

Original language	English (US)
Pages (from-to)	467-493
Number of pages	27
Journal	Journal of Statistical Physics
Volume	166
Issue number	3-4
DOIs	https://doi.org/10.1007/s10955-016-1608-7
State	Published - Feb 1 2017

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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AB - An important class of ‘physically relevant’ measures for dynamical systems with hyperbolic behavior is given by Sinai–Ruelle–Bowen (SRB) measures. We survey various techniques for constructing SRB measures and studying their properties, paying special attention to the geometric ‘push-forward’ approach. After describing this approach in the uniformly hyperbolic setting, we review recent work that extends it to non-uniformly hyperbolic systems.

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The Geometric Approach for Constructing Sinai–Ruelle–Bowen Measures

Abstract

All Science Journal Classification (ASJC) codes

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