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math.DS2008
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…
math.DS2008
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…
math.DS2008
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.