The strong closing lemma and Hamiltonian 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.

arXiv comment16 pages. V2: main theorem improved. We show that any perturbation through positive Hamiltonians leads to creation of periodic orbits