Preprint D75/2010
Hyperbolcity in the Volume-Preserving and Symplectic Scenario

Thiago Catalan | Arbieto, Alexander

**Keywords: **
Hyperbolic orbits | Volume preseving | symplectic | Palis Conjecture.

Hayashi has extended a result of Mane, proving that every element in $\mathcal{F}^1(M)$ satisfies Axioma A, i.e., every diffeomorphism $f$ with a neighborhood $\mathcal{U}$, where all periodic points of any $g\in\mathcal{U}$ are hyperbolic, it is an Axioma A diffeomorphism. Here, we prove an analogue result in the conservative and symplectic case, and using this we give a proof of the Palis conjecture in the conservative world.