$C^r$-Closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle
- Resource Type
- Working Paper
- Authors
- Gan, Shaobo; Shi, Yi
- Source
- Subject
- Mathematics - Dynamical Systems
- Language
For every $r\in\mathbb{N}_{\geq2}\cup\{\infty\}$, 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.