Sylvain Crovisier

Récurrence et généricité

Résumé.Nous montrons un lemme de connexion C1 pour les pseudo-orbites des difféomorphismes des variétés compactes. Nous explorons alors les conséquences pour les difféomorphismes C1-génériques. Par exemple, les difféomorphismes conservatifs C1-génériques (d’une variété connexe) sont transitifs. Abstract.We prove a C1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C1-generic diffeomorphisms. For instance, C1-generic conservative diffeomorphisms (on connected manifolds) are transitive.

Periodic points and homoclinic classes

We prove that there is a residual subset

Partial hyperbolicity and homoclinic tangencies

\mathcal{I}

Diffeomorphisms with positive metric entropy

of

Internal perturbations of homoclinic classes: non-domination, cycles, and self-replication

{\rm Diff}^1({\it M})

Recurrence and genericity

such that any homoclinic class of a diffeomorphism

Transitivity and Topological Mixing for \({C}^{1}\) Diffeomorphisms

f\in \mathcal{I}

CENTER MANIFOLDS FOR PARTIALLY HYPERBOLIC SETS WITHOUT STRONG UNSTABLE CONNECTIONS

having saddles of indices

Denjoy constructions for fibered homeomorphisms of the torus

\alpha

Pseudo-rotations of the closed annulus: variation on a theorem of J Kwapisz

and