On the number of noncontractible periodic orbits in Hamiltonian dynamics
Abstract
Abstract In this paper, we treat noncontractible periodic orbits in Hamiltonian dynamics on symplectic manifolds. We prove that any Hamiltonian diffeomorphism has infinitely many simple noncontractible periodic orbits, provided that the Hamiltonian diffeomorphism has at least one periodic orbit of infinite order in the first homology group and the orbit has nontrivial local Floer cohomology. Our proof is an application of the equivariant Hamiltonian Floer cohomology.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Publisher
- Wiley
- Volume
- 113
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN