On the Hofer-Zehnder conjecture for non-contractible periodic orbits in Hamiltonian dynamics

In this paper, we treat an open problem related to the number of periodic orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds. Hofer-Zehnder conjecture states that a Hamiltonian diffeomorphisms has infinitely many periodic orbits if it has "homologically unnecessary periodic or...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Author Sugimoto, Yoshihiro
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.08.2023
Subjects
Homology
Isomorphism
Manifolds
Orbits
Online AccessGet full text

Cover

More Information
Summary:In this paper, we treat an open problem related to the number of periodic orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds. Hofer-Zehnder conjecture states that a Hamiltonian diffeomorphisms has infinitely many periodic orbits if it has "homologically unnecessary periodic orbits"". For example, non-contractible periodic orbits are homologically unnecessary periodic orbits because Floer homology of non-contractible periodic orbits is trivial. We prove Hofer-Zehnder conjecture for non-contractible periodic orbits for very wide classes of symplectic manifolds.
ISSN:2331-8422