In this review we survey the literature on mean-field coupled maps. We start with the early
works from the physics literature, arriving to some recent results from ergodic theory studying …

We consider random transformations $ T_\omega^ n:= T_ {\sigma^{n-1}\omega}\circ\cdots\
circ T_ {\sigma\omega}\circ T_\omega, $ where each map $ T_ {\omega} $ acts on a …

We use extreme value theory to estimate the probability of successive exceedances of a
threshold value of a time-series of an observable on several classes of chaotic dynamical …

We prove functional limit theorems for dynamical systems in the presence of clusters of large
values which, when summed and suitably normalised, get collapsed in a jump of the limiting …

A classical Borel Cantelli Lemma gives conditions for deciding whether an infinite number of
rare events will almost surely happen. In this article, we propose an extension of Borel …

We analyse the existence of limiting laws of rare events for dynamically generated stochastic
processes. We consider two-dimensional dynamical systems and observable functions …

We study analytically and numerically the extreme value distribution of observables defined
along the temporal evolution of a dynamical system. The convergence to the Gumbel law of …

We obtain quenched hitting distributions to be compound Poissonian for a certain class of
random dynamical systems. The theory is general and designed to accommodate non …

Suppose $(f,\mathcal {X},\mu) $ is a measure preserving dynamical system and
$\phi\colon\mathcal {X}\to\mathbb {R} $ a measurable function. Consider the maximum …

We establish the general equivalence between rare event process for arbitrary continuous
functions whose maximal values are achieved on non-trivial sets, and the entry times …