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

Zhihong Xia·Hua Zhang
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Abstract

We prove a $C^r$ closing lemma for a class of partially hyperbolic symplectic diffeomorphisms. We show that for a generic $C^r$ 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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Zhihong Xia, Hua Zhang. 2005-03-11. A $C^{r}$ Closing Lemma for a Class of Symplectic Diffeomorphisms. https://doi.org/10.1088/0951-7715%2F19%2F2%2F015

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