Dynamiques génériques : hyperbolicité et transitivité
Sur les feuilletages singuliers stables des variétés de dimension trois.
Connexions hétéroclines et généricité d'une infinité de puits et de sources
Feuilles compactes d’un feuilletage générique en codimension
Smooth conjugacy classes of circle diffeomorphisms with irrational rotation number
We prove the C¹-density of every -conjugacy class in the closed subset of diffeomorphisms of the circle with a given irrational rotation number.
On maximal transitive sets of generic diffeomorphisms
The C 1 generic diffeomorphism has trivial centralizer
Answering a question of Smale, we prove that the space of C 1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices
Local density of diffeomorphisms with large centralizers
Given any compact manifold , we construct a non-empty open subset of the space of -diffeomorphisms and a dense subset such that the centralizer of every diffeomorphism in is uncountable, hence non-trivial.
Generic diffeomorphisms on compact surfaces
We discuss the remaining obstacles to prove Smale's conjecture about the C¹-density of hyperbolicity among surface diffeomorphisms. Using a C¹-generic approach, we classify the possible pathologies that may obstruct the C¹-density of hyperbolicity. We show that there are essentially two types of obstruction: (i) persistence of infinitely many hyperbolic homoclinic classes and (ii) existence of a single homoclinic class which robustly exhibits homoclinic tangencies. In the course of our discussion,...
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