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A $C^{r}$ Closing Lemma for a Class of Symplectic Diffeomorphisms

Published 11 Mar 2005 in math.DS | (0503225v1)

Abstract: We prove a $Cr$ closing lemma for a class of partially hyperbolic symplectic diffeomorphisms. We show that for a generic $Cr$ symplectic diffeomorphism, $r =1, 2, ...,$, with two dimensional center and close to a product map, the set of all periodic points is dense.

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