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math.DS2001
On the uniform hyperbolicity of some nonuniformly hyperbolic systems
Jose F. Alves, Vitor Araujo, Benoit Saussol
We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonunif…
math.DS2001
Recurrence, dimensions and Lyapunov exponents
B. Saussol, S. Troubetzkoy, S. Vaienti
We show that the Poincaré return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times.