On the Hofer-Zehnder conjecture for non-contractible periodic orbits in Hamiltonian dynamics
Symplectic Geometry
2026-05-08 v4 Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2102.05273,
title = {On the Hofer-Zehnder conjecture for non-contractible periodic orbits in Hamiltonian dynamics},
author = {Yoshihiro Sugimoto},
journal= {arXiv preprint arXiv:2102.05273},
year = {2026}
}