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) Sebastian Van Strien - Imperial College,
Titre Conjugacy classes of unimodal real-analytic maps: on a question by Avila, Lyubich and De Melo
Horaire14:00 à 16:00

Avila-Lyubich-de Melo proved that the topological conjugacy classes of unimodal real-analytic maps are complex analytic manifolds, which laminate a neighbourhood of any such mapping without a neutral cycle. Their proof that the manifolds are complex analytic depends on the fact that they have codimension-one in the space of unimodal mappings.  In joint work with Trevor Clark, we show how to construct a “pruned polynomial-like mapping" associated to a real mapping. This gives a new complex extension of a real-analytic mapping.
The additional structure provided by this extension, makes it possible to generalize this result of Avila-Lyubich-de Melo to interval mappings with several critical points. Thus we show that the conjugacy classes are complex analytic manifolds whose codimension is determined by the number of critical points.
Building on these ideas, we believe we can show that in the space of unimodal mappings with negative Schwarzian derivative, the conjugacy classes laminate a neighbourhood of every mapping, answering a question of Avila-Lyubich-de Melo. Joint work with Trevor Clark. 

AdresseCampus Pierre et Marie Curie