$C^r$-Closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle

Abstract

For every $r\in {\mathbb{N}}_{\ge 2}\cup \{\infty \}$, we prove the $C^r$-closing lemma for general and conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle. In particular, it implies periodic points are dense for $C^r$-generic conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle.

References in corpus (1)

• Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group