Frédéric Paccaut, Professor Assistant, University of Piccardy

"an introduction to dynamical systems : basic definitions and examples"

A dynamical system is an action of a map on a space. An orbit is the set of iterates of this map on a point of the space. The main question one can ask about a dynamical system is : how do the orbits behave ? The aim of this short course will be to explain how a purely deterministic dynamical system may give rise to random behaviors. Basic notions of topological and measurable dynamics will be introduced and illustrated on examples : dynamics on the interval, on the circle, on the shift space.