Related papers: Decay of correlations and central limit theorem fo…

Let f be a holomorphic automorphism of positive entropy on a compact Kaehler surface. We show that the equilibrium measure of f is exponentially mixing. The proof uses some recent development on the pluripotential theory. The result also…

Let $X$ be a compact complex non-K\"ahler manifold and $f$ a dominant meromorphic self-map of $X$. Examples of such maps are self-maps of Hopf manifolds, Calabi-Eckmann manifolds, non-tori nilmanifolds and their blowups. We prove that if…

Let $f$ be a holomorphic automorphism of a compact K\"ahler manifold with simple action on cohomology and $\mu$ its unique measure of maximal entropy. We prove that $\mu$ is exponentially mixing of all orders for all d.s.h.\ observables,…

We consider multimodal C^3 interval maps f satisfying a summability condition on the derivatives D_n along the critical orbits which implies the existence of an absolutely continuous f -invariant probability measure mu. If f is…

We prove general mixing theorems for sequences of meromorphic maps on compact K\"ahler manifolds. We deduce that the bifurcation measure is exponentially mixing for a family of rational maps of $\mathbb{P}^q(\mathbb{C})$ endowed with…

We study the dynamics of meromorphic maps for a compact Kaehler manifold X. More precisely, we give a simple criterion that allows us to produce a measure of maximal entropy. We can apply this result to bound the Lyapunov exponents. Then,…

We consider the unique measure of maximal entropy of an automorphism of a compact K{\"a}hler manifold with simple action on cohomology. We show that it is exponentially mixing of all orders with respect to H{\"o}lder observables. It follows…

Let $f$ be a complex H\'enon map and $\mu$ its unique measure of maximal entropy. We prove that $\mu$ is exponentially mixing of all orders for all (not necessarily bounded) plurisubharmonic observables, and that all plurisubharmonic…

We show, for a class of automorphisms of C^k, that their equilibrium measures are exponentially mixing. In particular, this holds for (generalized) Henon maps.

Let $f$ be a dominating meromorphic self-map of a compact K\"{a}hler manifold. Assume that the topological degree of $f$ is larger than the other dynamical degrees. We give estimates of the dimension of the equilibrium measure of $f$, which…

Let f be a meromorphic self-map on a compact Kaehler manifold whose topological degree is strictly larger than the other dynamical degrees. We show that repelling periodic points are equidistributed with respect to the equilibrium measure…

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 prove exponential estimates for plurisubharmonic functions with respect to Monge-Ampere measures with Holder continuous potential. As an application, we obtain several stochastic properties for the equilibrium measures associated to…

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the…

We prove weak laws of large numbers and central limit theorems of Lindeberg type for empirical centres of mass (empirical Fr\'echet means) of independent non-identically distributed random variables taking values in Riemannian manifolds. In…

This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of…

We show that any dominant meromorphic self-map f of a compact Kaehler manifold X is an Artin-Mazur map. More precisely, if P_n(f) is the number of its isolated periodic points of period n (counted with multiplicity), then P_n(f) grows at…

We consider a class of non-conformal expanding maps on the $d$-dimensional torus. For an equilibrium measure of an H\"older potential, we prove an analogue of the Central Limit Theorem for the fluctuations of the logarithm of the measure of…

We show that the measure of maximal entropy of every complex H\'enon map is exponentially mixing of all orders for H\''older observables. As a consequence, the Central Limit Theorem holds for all H\''older observables.