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$C^r$-Closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle (2004.06855v2)
Published 15 Apr 2020 in math.DS
Abstract: For every $r\in\mathbb{N}_{\geq2}\cup{\infty}$, we prove the $Cr$-closing lemma for general and conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle. In particular, it implies periodic points are dense for $Cr$-generic conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle.
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