Non-contractible periodic orbits in Hamiltonian dynamics on tori

TL;DR

This paper proves that having one non-degenerate, non-contractible periodic orbit in Hamiltonian dynamics on a torus guarantees infinitely many such orbits, revealing rich dynamical complexity.

Contribution

It establishes a new link between the existence of a single non-contractible periodic orbit and the proliferation of infinitely many such orbits in Hamiltonian systems on tori.

Findings

Presence of one non-degenerate, non-contractible orbit implies infinitely many such orbits.

The result applies specifically to Hamiltonian systems on the standard symplectic torus.

It advances understanding of periodic orbit multiplicity in symplectic topology.

Abstract

We show that the presence of one non-degenerate, non-contractible periodic orbit of a Hamiltonian on the standard symplectic torus implies the existence of infinitely many simple non-contractible periodic orbits.