Related papers: Statistical stability for robust classes of maps w…

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 probability measures describing the statistical…

We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…

We consider families of transformations in multidimensional Riemannian manifolds with non-uniformly expanding behavior. We give sufficient conditions for the continuous variation (in the $L^1$-norm) of the densities of absolutely continuous…

We construct SRB measures for endomorphisms satisfying conditions far weaker than the non-uniformly expansion. As a consequence, the definition of non-uniformly expanding map can be weakened. We also prove the existence of an absolutely…

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 the SRB measure varies continuously with the…

We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our technique is based on inducing the non-uniformly expanding system to a uniformly expanding one, and on showing…

We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…

For a large class of nonuniformly expanding maps of $\Bbb R^m$, with indifferent fixed points and unbounded distorsion and non necessarily Markovian, we construct an absolutely continuous invariant measure. We extend to our case techniques…

Let $f : [0, 1] \to [0, 1]$ be a piecewise expanding unimodal map of class $C^{k+1}$, with $k \geq 1$, and $\mu = \rho dx$ the (unique) SRB measure associated to it. We study the regularity of $\rho$. In particular, points $\mathcal{N}$…

For a class of dynamical systems, called the axiom-A systems, Sinai, Ruelle and Bowen showed the existence of an invariant measure (SRB measure) weakly attracting the temporal average of any initial distribution that is absolutely…

We prove the existence of SRB measures for diffeomorphisms where a positive volume set of initial conditions satisfy an "effective hyperbolicity" condition that guarantees certain recurrence conditions on the iterates of Lebesgue measure.…

We prove that a $C^1$ hyperbolic map whose differential is regular enough has an SRB measure. The precise regularity condition is weaker than H{\"o}lder and was mentionned by various authors through the developement of expanding and…

We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic…

We prove existence of equilibrium states with special properties for a class of distance expanding local homeomorphisms on compact metric spaces and continuous potentials. Moreover, we formulate a C$^1$ generalization of Pesin's Entropy…

We study the existence of SRB measures of C 2 diffeomorphisms for attractors whose bundles admit Holder continuous invariant (non-dominated) splittings. We prove the existence when one subbundle has the non-uniform expanding property on a…

For any C1 expanding map f of the circle we study the equilibrium states for the potential -log |f'|. We formulate a C1 generalization of Pesin's Entropy Formula that holds for all the SRB measures if they exist, and for all the…

We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of discontinuities and of non-degenerate critical points and/or singular points with infinite derivative, and satisfy…

We consider a robust class of random non-uniformly expanding local homeomorphisms and H\"older continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and…