Entropic stability beyond partial hyperbolicity

Details Entropic stability beyond partial hyperbolicity Entropic stability beyond partial hyperbolicity

2011-03-14

arxiv.org/abs/1103.2707v1

Mathematics

Dynamical Systems

27 pages, 4 figures

Scientific paper

We analyze a class of deformations of Anosov diffeomorphisms: these $C^0$-small, but $C^1$-macroscopic deformations break the topological conjugacy class but leave the high entropy dynamics unchanged. More precisely, there is a partial conjugacy between the deformation and the original Anosov system that identifies all invariant probability measures with entropy close to the maximum. We also establish expansiveness around those measures. This class of deformations contains many of the known nonhyperbolic robustly transitive diffeomorphisms. In particular, we show that it includes a class of nonpartially hyperbolic, robustly transitive diffeomorphisms described by Bonatti and Viana.

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