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Journal of Statistical Physics

, Volume 166, Issue 3–4, pp 467–493 | Cite as

The Geometric Approach for Constructing Sinai–Ruelle–Bowen Measures

  • Vaughn Climenhaga
  • Stefano Luzzatto
  • Yakov PesinEmail author
Article

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.

Keywords

Non-uniform hyperbolicity Dominated splitting Attractor Physical measures SRB measures 

Notes

Acknowledgments

V.C. was partially supported by NSF Grant DMS-1362838. Ya.P. was partially supported by NSF Grant DMS-1400027. V.C. and Ya.P. would like to thank Erwin Schrödinger Institute and ICERM where the part of the work was done for their hospitality.

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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Abdus Salam International Centre for Theoretical Physics (ICTP)TriesteItaly
  3. 3.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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