Written by a team of international experts, Extremes and Recurrence in Dynamical Systems
presents a unique point of view on the mathematical theory of extremes and on its …

The rst occurrence time of a rare event in a mixing process typically has a distribution which
can be well approximated by the exponential law. In this paper we review recent theorems …

In this paper we provide general estimates for the errors between the distribution of the first,
and more generally, the K th return time (suitably rescaled) and the Poisson law for …

Given an ergodic dynamical system (X, T, μ), and U⊂ X measurable with μ (U)> 0, let μ (U) τ
U (x) denote the normalized hitting time of x∈ X to U. We prove that given a sequence (U n) …

We prove that a hitting time of a mixing dynamical system can be sharply approximated by
an exponential random variable. More precisely, we prove that there exists four strictly …

We study the number of visits to balls Br (x), up to time t/μ (Br (x)), for a class of non-uniformly
hyperbolic dynamical systems, where μ is the Sinai–Ruelle–Bowen measure. Outside a set …

We show that distributional and weak functional limit theorems for ergodic processes often
hold for arbitrary absolutely continuous initial distributions. This principle is illustrated in the …

This book is devoted to the subject commonly called Chaotic Dynamics, namely the study of
complicated behavior in time of maps and? ows, called dynamical systems. The theory of …

We prove a dichotomy for Manneville–Pomeau maps f:[0, 1]→[0, 1]: given any point ζ∈[0, 1],
either the Rare Events Point Processes (REPP), counting the number of exceedances …

Dispersing billiards introduced by Sinai are uniformly hyperbolic and have strong statistical
properties (exponential decay of correlations and various limit theorems). However, if the …