The strong closing lemma and Hamiltonian pseudo-rotations. (English) Zbl 07924656
Summary: We prove a \(C^{\infty}\) closing lemma for a class of Hamiltonian diffeomorphisms which includes all pseudo-rotations of \(\mathbb{C} P^n\) as well as all Anosov-Katok pseudo-rotations. This implies, in particular, that the strong \(C^{\infty}\) closing property, as formulated by Irie, holds for this class of Hamiltonian diffeomorphisms.
MSC:
| 53D40 | Symplectic aspects of Floer homology and cohomology |
| 37C20 | Generic properties, structural stability of dynamical systems |
| 53D10 | Contact manifolds (general theory) |
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