Séminaires : Séminaire de Systèmes Dynamiques

Equipe(s) : gd,
Responsables :H. Eliasson, B. Fayad, R. Krikorian, P. Le Calvez
Email des responsables :
Salle : 15-25-502
Adresse :Campus Pierre et Marie Curie

Archive avant 2015

Hébergé par le projet Géométrie et Dynamique de l’IMJ

Orateur(s) Artur Avila (with Zhiyuan Zhang) - Univ. Zürich,
Titre Renormailzation, fractal geometry and the Newhouse phenomenon
Horaire14:00 à 16:00

As discovered by Poincaré in the end of the 19th century, even small perturbations of very regular dynamical systems may display chaotic features, due to complicated interactions near a homoclinic point. In the 1960's Smale attempted to understand such dynamics in term of a stable model, the horseshoe, but this was too optimistic.Indeed, Newhouse showed that even in only two  dimensions, a homoclinic bifurcation gives rise to particular wild dynamics, such as the generic presence  of infinitely many attractors. This Newhouse phenomenon is associated to a renormalization mechanism, but also with particular geometric properties of some fractal sets within a Smale horseshoe. When considering two-dimensional complex dynamics those fractal sets become much more beautiful but unfortunately also more difficultto handle.

AdresseCampus Pierre et Marie Curie