Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on $T^*\T^n$ with application to non convex Hamiltonian systems

Abstract

In this paper, we show the existence of non contractible periodic orbits in Hamiltonian systems defined on $T^*\T^n$ separating two Lagrangian tori under certain cone assumption. Our result answers a question of Polterovich in \cite{P} in a sharp way. As an application, we find periodic orbits of almost all the homotopy types on a dense set of energy level in Lorentzian type mechanical Hamiltonian systems defined on $T^*\T^2$. This solves a problem of Arnold in \cite{A}.

simplification of the construction

References in corpus (3)

• Non-contractible Periodic Orbits in Hamiltonian Dynamics on Closed Symplectic Manifolds
• Non-contractible periodic orbits, Gromov invariants, and Floer-theoretic torsions
• Spectral invariants towards a Non-convex Aubry-Mather theory

Cited by in corpus (5)

• Non-contractible Periodic Orbits in Hamiltonian Dynamics on Closed Symplectic Manifolds
• Symplectic deformations of Floer homology and non-contractible periodic orbits in twisted disc bundles
• Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories
• Heavy subsets and non-contractible trajectories
• Non-contractible orbits for Hamiltonian functions on Riemann surfaces