Séminaires : Séminaire de Systèmes Dynamiques

Equipe(s) : gd,
Responsables :H. Eliasson, B. Fayad, R. Krikorian, P. Le Calvez
Email des responsables :
Salle : ZOOM ID 857 3353 2552 (code : 666061)
Adresse :Campus Pierre et Marie Curie

Archive avant 2015

Hébergé par le projet Géométrie et Dynamique de l’IMJ

Orateur(s) Hana Rodriguez Hertz - SUSTech (Chine),
Titre Minimality and stable ergodicity
Horaire14:00 à 15:30

We prove that generically in $\diff^{1}_{m}(M)$, if an expanding $f$-invariant foliation $W$ of dimension $u$ is minimal and there is a periodic point of unstable index $u$, the foliation is stably minimal. By this we mean there is a $C^{1}$-neighborhood $\U$ of $f$ such that for all $C^{2}$-diffeomorphisms $g\in \U$, the $g$-invariant continuation of $W$ is minimal. In particular, all such $g$ are topologically mixing. Moreover, all such $g$ have a hyperbolic ergodic component of the volume measure $m$ which is essentially dense. This component is, in fact, Bernoulli.

We provide new examples of stably minimal diffeomorphisms which are not partially hyperbolic.


SalleZOOM ID 857 3353 2552 (code : 666061)
AdresseCampus Pierre et Marie Curie