This scientific project is in the domain of the probabilistic and statistical properties of dynamical

systems. We can identify two main axes of theoretical investigation which very often share questions,

methods and objectives.

•The first concerns deterministic dynamical systems

. In recent years efforts of mathematicians have been directed to study and understand systems beyond uniform hyperbolicity; notions of non-uniformly hyperbolic attractors, partially hyperbolic attractors, non-uniformly

expanding maps and flows have been introduced. These recent developments concern dynamical systems preserving a probability measure as well as dynamical systems preserving an infinite measure.

•The second deals with perturbations of deterministic system, which induces an additional source of randomness and allows us to define new models such as sequential dynamical systems, non-stationary, quenched and fibred dynamical systems, etc. In this context the proofs of limit theorems show new difficulties and call for new approaches and techniques or adaptations of previous methods.