Hyperbolicity in the Volume Preserving Scenario

Details Hyperbolicity in the Volume Preserving Scenario Hyperbolicity in the Volume Preserving Scenario

2010-04-10

arxiv.org/abs/1004.1664v2

Mathematics

Dynamical Systems

We improve the presentation of the previous version and correct some issues about the symplectic case.

Scientific paper

Hayashi has extended a result of Ma\~n\'e, proving that every diffeomorphism
$f$ which has a $C^1$-neighborhood $\mathcal{U}$, where all periodic points of
any $g\in\mathcal{U}$ are hyperbolic, it is an Axiom A diffeomorphism. Here, we
prove the analogous result in the volume preserving scenario.

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