We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms – the tangent bundle splits into two invariant subbundles, one of which is uniformly… (More)

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 general conditions they… (More)

We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of… (More)

We consider families of transformations in multidimensional Riemannian manifolds with non-uniformly expanding behavior. We give sufficient conditions for the continuous variation (in theL1-norm) of… (More)

We consider dynamical systems on compact manifolds, which are local diffeomorphisms outside an exceptional set (a compact submanifold). We are interested in analyzing the relation between the… (More)

Abstract. We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions, which in particular guarantee the existence of SRB measures, we prove that the entropy of… (More)

— We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM = E cu⊕Es, for which the centre-unstable direction E expands non-uniformly on some local… (More)

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 behaviour such… (More)

We consider open sets of maps in a manifold M exhibiting non-uniform expanding behaviour in some domain S ⊂ M . Assuming that there is a forward invariant region containing S where each map has a… (More)