On the uniform hyperbolicity of some nonuniformly hyperbolic systems

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

2001-11-09

arxiv.org/abs/math/0111110v1

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

Mathematics

Dynamical Systems

Scientific paper

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
are necessarily uniformly expanding. We also present a version of this result
for diffeomorphisms with nonuniformly hyperbolic sets.

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