Weak Pseudo-Physical Measures and Pesin's Entropy Formula for Anosov C1 diffeomorphisms
Dynamical Systems
2018-03-01 v1
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.
Keywords
Cite
@article{arxiv.1601.06279,
title = {Weak Pseudo-Physical Measures and Pesin's Entropy Formula for Anosov C1 diffeomorphisms},
author = {Eleonora Catsigeras and Marcelo Cerminara and Heber Enrich},
journal= {arXiv preprint arXiv:1601.06279},
year = {2018}
}