An almost existence theorem for non-contractible periodic orbits in cotangent bundles

Abstract

Assume M is a closed connected smooth manifold and H:T^*M->R a smooth proper function bounded from below. Suppose the sublevel set {H<d} contains the zero section and αis a non-trivial homotopy class of free loops in M. Then for almost every s>=d the level set {H=s} carries a periodic orbit z of the Hamiltonian system (T^*M,ω_0,H) representing α. Examples show that the condition that {H<d} contains M is necessary and almost existence cannot be improved to everywhere existence.

9 pages, 4 figures. v2: corrected typos

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