126 citations
- Université Sorbonne Paris NordFR135 papers
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4 papers · 2 filters
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…
Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds
François Béguin, Sylvain Crovisier, Frédéric Le Roux
We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable un…
The C1 generic diffeomorphism has trivial centralizer
Christian Bonatti, Sylvain Crovisier, Amie Wilkinson
Answering a question of Smale, we prove that the space of C1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.