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arXiv · 1601.06279

Weak Pseudo-Physical Measures and Pesin's Entropy Formula for Anosov C1 diffeomorphisms

Eleonora Catsigeras·Marcelo Cerminara·Heber Enrich
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Abstract

We consider C1 Anosov diffeomorphisms on a compact Riemannian manifold. We define the weak pseudo-physical measures, which include the physical measures when these latter exist. We prove that ergodic weak pseudo-physical measures do exist, and that the set of invariant probability measures that satisfy Pesin's Entropy Formula is the weak*-closed convex hull of the ergodic weak pseudo-physical measures. In brief, we give in the C1-scenario of uniform hyperbolicity, a characterization of Pesin's Entropy Formula in terms of physical-like properties.

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Eleonora Catsigeras, Marcelo Cerminara, Heber Enrich. 2016-01-23. Weak Pseudo-Physical Measures and Pesin's Entropy Formula for Anosov C1 diffeomorphisms. https://doi.org/10.1090/conm%2F698%2F13979

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