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arXiv · 1405.6194

Non-stationary non-uniform hyperbolicity: SRB measures for dissipative maps

Vaughn Climenhaga·Dmitry Dolgopyat·Yakov Pesin
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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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Vaughn Climenhaga, Dmitry Dolgopyat, Yakov Pesin. 2014-05-23. Non-stationary non-uniform hyperbolicity: SRB measures for dissipative maps. https://doi.org/10.1007/s00220-016-2710-z

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