On the uniform hyperbolicity of some nonuniformly hyperbolic systems
On the uniform hyperbolicity of some nonuniformly hyperbolic systems
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 …