2001/11/09 by Jose F. Alves, Vitor Araujo, Benoit Saussol
Mathematics · #math.DS #msc:58F15 #msc:58F99
published as Proc. Amer. Math. Soc. 131 (2003), 1303-1309.
arxiv created 2001/11/09 · arxiv updated 2009/11/30
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.