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.
A $C^{r}$ Closing Lemma for a Class of Symplectic Diffeomorphisms
A $C^{\infty}$ closing lemma on torus
On the $C^{\infty}$ closing lemma for Hamiltonian flows on symplectic $4$-manifolds
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