On the number of noncontractible periodic orbits in Hamiltonian dynamics

Key Points

• This paper aims to explore noncontractible periodic orbits in Hamiltonian dynamics on symplectic manifolds.
• Proving results based on properties of Hamiltonian diffeomorphisms
• Analyzing periodic orbits of infinite order in the first homology group
• Applying equivariant Hamiltonian Floer cohomology to the problem.
• Demonstrated that Hamiltonian diffeomorphisms possess infinitely many simple noncontractible periodic orbits when they have at least one periodic orbit of infinite order.
• Established conditions involving nontrivial local Floer cohomology that support this finding.