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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…