In broad terms, the goal of dynamics is to describe the long-term evolution of systems for
which an" infinitesimal" evolution rule, such as a differential equation or the iteration of a …

The book aims to provide a global perspective of this theory and make it easier for the
reader to digest the growing literature on this subject. This is not the first book on the subject …

We consider discrete time dynamical systems and show the link between Hitting Time
Statistics (the distribution of the first time points land in asymptotically small sets) and …

We prove an almost sure invariance principle that is valid for general classes of
nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time …

In Young towers with sufficiently small tails, the Birkhoff sums of Hölder continuous functions
satisfy a central limit theorem with speed O (1/n), and a local limit theorem. This implies the …

We prove statistical limit laws for sequences of Birkhoff sums of the type∑ j= 0 n− 1 vn∘ T nj
where T n is a family of nonuniformly hyperbolic transformations. The key ingredient is a new …

In recent years, substantial progress was made towards understanding convergence of fast-
slow deterministic systems to stochastic differential equations. In contrast to more classical …

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 …

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 …

For a class of partially hyperbolic Ck, k> 1 diffeomorphisms with circle center leaves we
prove the existence and finiteness of physical (or Sinai–Ruelle–Bowen) measures, whose …