On the uniform hyperbolicity of some nonuniformly hyperbolic systems

Alves, José; Araújo, Vítor; Saussol, Benoît

doi:10.1090/S0002-9939-02-06857-0

On the uniform hyperbolicity of some nonuniformly hyperbolic systems
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by José F. Alves, Vítor Araújo and Benoît Saussol PDF

Proc. Amer. Math. Soc. 131 (2003), 1303-1309 Request permission

Abstract:

We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability (probability one with respect to every invariant probability measure) are necessarily uniformly expanding. We also present a version of this result for diffeomorphisms with nonuniformly hyperbolic sets.

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