8 papers · 1 filter
Partial hyperbolicity far from homoclinic bifurcations
Sylvain Crovisier
We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensi…
Nonuniform hyperbolicity for C^1-generic diffeomorphisms
Flavio Abdenur, Christian Bonatti, Sylvain Crovisier
We study the ergodic theory of non-conservative C^1-generic diffeomorphisms. First, we show that homoclinic classes of arbitrary diffeomorphisms exhibit ergodic measures whose supp…
C1-generic conservative diffeomorphisms have trivial centralizer
Christian Bonatti, Sylvain Crovisier, Amie Wilkinson
We prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving diffeomorphisms of connected manifolds both contain residual subsets of diffeomorphisms whose centrali…
Local density of diffeomorphisms with large centralizers
Christian Bonatti, Sylvain Crovisier, Gioia Vago +1
Given any compact manifold M, we construct a non-empty open subset O of the space of C^1-diffeomorphisms of M and a dense subset D of O such that the centralizer of every diffeomor…
Denjoy constructions for fibred homeomorphisms of the torus
François Béguin, Sylvain Crovisier, Tobias Jaeger +1
We construct different types of quasiperiodically forced circle homeomorphisms with transitive but non-minimal dynamics. Concerning the recent Poincaré-like classification for this…
The centralizer of a C1 generic diffeomorphism is trivial
Christian Bonatti, Sylvain Crovisier, Amie Wilkinson
In this announcement, we describe the solution in the C1 topology to a question asked by S. Smale on the genericity of trivial centralizers: the set of diffeomorphisms of a compact…