Automorphismes d'entropie positive, le cas des surfaces rationnelles

Abstract

A complex compact surface which carries an automorphism of positive topological entropy has been proved by Cantat to be a torus, a K3 surface, an Enriques surface or a non-minimal rational surface. We deal with results obtained in this last case. After some recalls on birational maps, algebraic geometry and dynamic, we will speak about Bedford and Kim's works, but also about McMullen's work and more recently about Grivaux and the author's work. These notes have been written for four talks given at IMPA in february/march 2010.