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 …

This paper reviews recent progress that has been made in the study of return times
distribution. We discuss recent results on the first return time for systems with various mixing …

For non-uniformly hyperbolic maps of the interval with exponential decay of correlations we
prove that the law of closest return to a given point when suitably normalized is almost surely …

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 an upper bound for the error in the exponential approximation of the hitting time
law of a rare event in $\alpha $-mixing processes with exponential decay, $\phi $-mixing …

We present bounds of the error of the exponential approximation of the rst occurrence time
of a rare event in a stationary stochastic process with nite alphabet with-mixing property with …

We prove that the return time statistics of a dynamical system do not change if one passes to
an induced (ie first return) map. We apply this to show exponential return time statistics in (i) …

Previously it has been shown that some classes of mixing dynamical systems have limiting
return times distributions that are almost everywhere Poissonian. Here we study the …

We present some recurrence results in the context of ergodic theory and dynamical systems.
The main focus will be on smooth dynamical systems, in particular, those with some …

The global statistics of the return times of a dynamical system can be described by a new
spectrum of generalized dimensions. Comparison with the usual multifractal analysis of …