The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

Abstract

Let $M$ be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian $H:T^{\ast }M\to \mathbb{R}$ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if $M$ is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of $H$.

21 pages. We have generalized the results of the previous version to a larger class of manifolds and of energy values. Remarks and comments are very welcome. To appear on Journal of Topology and Analysis

References in corpus (1)

• On the existence of periodic orbits for magnetic systems on the two-sphere

Cited by in corpus (8)

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• On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus
• On Tonelli periodic orbits with low energy on surfaces
• Periodic orbits in virtually contact structures
• On the rigidity of Zoll magnetic systems on surfaces