Although individual orbits of chaotic dynamical systems are by definition unpredictable, the
average behavior of typical trajectories can often be given a precise statistical description …

We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary
dimension, possibly having discontinuities and/or critical sets, and show that under some …

We prove statistical limit laws for sequences of Birkhoff sums of the type∑ j= 0 n− 1 vn∘ T nj
where T n is a family of nonuniformly hyperbolic transformations. The key ingredient is a new …

A classic approach in dynamical systems is to use particular geometric structures to deduce
statistical properties, for example the existence of invariant measures with stochastic-like …

We give both sufficient conditions and necessary conditions for the stochastic stability of
nonuniformly expanding maps either with or without critical sets. We also show that the …

We estimate the speed of decay of correlations for general nonuniformly expanding
dynamical systems, using estimates on the time the system takes to become really …

For a class of partially hyperbolic Ck, k> 1 diffeomorphisms with circle center leaves we
prove the existence and finiteness of physical (or Sinai–Ruelle–Bowen) measures, whose …

We show a linear response statement for fixed points of a family of Markov operators, which
are perturbations of mixing and regularizing operators. We apply the statement to random …

We establish bounds for the measure of deviation sets associated to continuous
observables with respect to not necessarily invariant weak Gibbs measures. Under some …

We consider families of transformations in multidimensional Riemannian manifolds with non-
uniformly expanding behaviour. We give sufficient conditions for the continuous variation (in …