The geometric approach for constructing Sinai-Ruelle-Bowen measures

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.

arXiv comment30 pages

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Cited by in corpus (8)

• Applications of large deviation theory in geophysical fluid dynamics and climate science
• Statistical stability of mostly expanding diffeomorphisms
• The Almost Sure Essential Spectrum of the Doubling Map Model is Connected
• SRB and equilibrium measures via dimension theory
• Gibbs measures for hyperbolic attractors defined by densities
• SRB measures for C $\infty$ surface diffeomorphisms
• Open sets of partially hyperbolic skew products having a unique SRB measure
• Self-adjoint Laplacians on partially and generalized hyperbolic attractors