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

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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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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, USA

    Vaughn Climenhaga

  2. Department of Mathematics, University of Maryland, College Park, MD, USA

    Dmitry Dolgopyat

  3. Department of Mathematics, Pennsylvania State University, State College, PA, USA

    Yakov Pesin

Authors
  1. Vaughn Climenhaga
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  2. Dmitry Dolgopyat
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  3. Yakov Pesin
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Corresponding author

Correspondence to Vaughn Climenhaga.

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Communicated by H.-T. Yau

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Climenhaga, V., Dolgopyat, D. & Pesin, Y. Non-Stationary Non-Uniform Hyperbolicity: SRB Measures for Dissipative Maps. Commun. Math. Phys. 346, 553–602 (2016). https://doi.org/10.1007/s00220-016-2710-z

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  • DOI: https://doi.org/10.1007/s00220-016-2710-z

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