Related papers: Stochastic-like behaviour in nonuniformly expandin…

We discuss recent results on decay of correlations for non-uniformly expanding maps. Throughout the discussion, we address the question of why different dynamical systems have different rates of decay of correlations and how this may…

Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and…

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 admit an induced Markov tower structure…

We consider random perturbations of non-uniformly expanding maps, possibly having a non-degenerate critical set. We prove that, if the Lebesgue measure of the set of points failing the non-uniform expansion or the slow recurrence to the…

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…

We give conditions under which nonuniformly expanding maps exhibit lower bounds of polynomial type for the decay of correlations and for a large class of observables. We show that if the Lasota-Yorke type inequality for the transfer…

We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on…

We consider the general question of estimating decay of correlations for non-uniformly expanding maps, for classes of observables which are much larger than the usual class of Holder continuous functions. Our results give new estimates for…

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 expanding. Our method can deal with fast decays, such as exponential or…

In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…

A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…

For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…

Intermittent maps of Pomeau-Manneville type are well-studied in one-dimension, and also in higher dimensions if the map happens to be Markov. In general, the nonconformality of multidimensional intermittent maps represents a challenge that…

In this article, we address the decay of correlations for dynamical systems that admit an induced weak Gibbs Markov map (not necessarily full branch). Our approach generalizes L.-S. Young's coupling arguments to estimate the decay of…

For a certain parametrized family of maps on the circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit…

We study the rate of decay of correlations for equilibrium states associated to a robust class of non-uniformly expanding maps where no Markov assumption is required. We show that the Ruelle-Perron-Frobenius operator acting on the space of…

We prove a quenched almost sure invariance principle for certain classes of random distance expanding dynamical systems which do not necessarily exhibit uniform decay of correlations.

We introduce a family of area preserving generalized baker's transformations acting on the unit square and having sharp polynomial rates of mixing for Holder data. The construction is geometric, relying on the graph of a single variable…

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 as large deviations or decay of…