Séminaires : Séminaire de Systèmes Dynamiques

 Equipe(s) : gd, Responsables : H. Eliasson, B. Fayad, R. Krikorian, P. Le Calvez Email des responsables : Salle : salle 15-25-502 Adresse : Campus Pierre et Marie Curie Description Archive avant 2015 Hébergé par le projet Géométrie et Dynamique de l’IMJ

 Orateur(s) Alejandro Passeggi - Montevideo, Titre topological and rotational aspects of dissipative homoclinical bifurcations. Date 14/06/2019 Horaire 14:00 à 16:00 Résume The Rotation set of an annular homeomorphism is a natural invariant from which one aims to describe the dynamic. In the dissipative case, when considered for annular attractors, this invariant given by compact intervals of $\R$ in general fails to be continuous. The first part of this talk is intended to discuss this fact, and present results ensuring the continuity of the map depending on the topological properties of the attractor. Then, we study the developed criteria on $C^2$ one-parameter families of annular attractors undergoing homoclinical bifurcations. We show that under suitable $C^2$ open conditions for the homoclinic bifurcations, the rotation set will vary continuously. Moreover, for these families, we obtain that the prime-end rotation number coincide with $\max \rho(F_t)$, and hence depends continuously upon the parameter t. Salle salle 15-25-502 Adresse Campus Pierre et Marie Curie