Non-Stationary Non-Uniform Hyperbolicity: SRB Measures for Dissipative Maps

Vaughn Climenhaga; Dmitry Dolgopyat; Yakov Pesin

doi:10.1007/s00220-016-2710-z

Non-Stationary Non-Uniform Hyperbolicity: SRB Measures for Dissipative Maps

Vaughn Climenhaga, Dmitry Dolgopyat, Yakov Pesin

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15 Scopus citations

Abstract

We prove the existence of SRB measures for diffeomorphisms where a positive volume set of initial conditions satisfy an “effective hyperbolicity” condition that guarantees certain recurrence conditions on the iterates of Lebesgue measure. We give examples of systems that do not admit a dominated splitting but can be shown to have SRB measures using our methods.

Original language	English (US)
Pages (from-to)	553-602
Number of pages	50
Journal	Communications In Mathematical Physics
Volume	346
Issue number	2
DOIs	https://doi.org/10.1007/s00220-016-2710-z
State	Published - Sep 1 2016

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We prove the existence of SRB measures for diffeomorphisms where a positive volume set of initial conditions satisfy an “effective hyperbolicity” condition that guarantees certain recurrence conditions on the iterates of Lebesgue measure. We give examples of systems that do not admit a dominated splitting but can be shown to have SRB measures using our methods.",

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Non-Stationary Non-Uniform Hyperbolicity: SRB Measures for Dissipative Maps

Abstract

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