The strong closing lemma and Hamiltonian pseudo-rotations

TL;DR

This paper proves a strong closing property for a class of Hamiltonian diffeomorphisms, including pseudo-rotations of projective spaces and Anosov-Katok pseudo-rotations, advancing understanding of their dynamical behavior.

Contribution

It establishes the strong $C^ abla$ closing property for Hamiltonian diffeomorphisms encompassing pseudo-rotations and Anosov-Katok examples, extending previous results.

Findings

Proves the strong $C^ abla$ closing property for specific Hamiltonian diffeomorphisms.

Includes all pseudo-rotations of projective spaces in the class.

Applies to all Anosov-Katok pseudo-rotations.

Abstract

We prove the strong $C^\infty$ closing property, as formulated by Irie, for a class of Hamiltonian diffeomorphisms which includes all pseudo-rotations of projective spaces as well as all Anosov-Katok pseudo-rotations.