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 $H$.

arXiv comment21 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

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Cited by in corpus (9)

• Open problems and questions about geodesics
• The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere
• On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus
• Invariance of symplectic cohomology and twisted cotangent bundles over surfaces
• Symplectic deformations of Floer homology and non-contractible periodic orbits in twisted disc bundles
• Two closed orbits for non-degenerate Reeb flows
• On Tonelli periodic orbits with low energy on surfaces
• Periodic orbits in virtually contact structures
• On the rigidity of Zoll magnetic systems on surfaces