5 papers
Recurrence rate in rapidly mixing dynamical systems
Benoit Saussol
For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of co…
Products of non-stationary random matrices and Multiperiodic equations of several scaling factors
Ai-Hua Fan, Benoit Saussol, Joerg Schmeling
Let be a real number and $M: \mathbb{R}\to {\rm GL(\CC^d)}$ be a uniformly almost periodic matrix-valued function. We study the asymptotic behavior of the product $$ P_n(x) =…
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…
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.
Return time statistics via inducing
Henk Bruin, Benoit Saussol, Serge Troubetzkoy +1
We prove that return time statistics of a dynamical system do not change if one passes to an induced (i.e. first return) map. We apply this to show exponential return time statisti…