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arXiv · 1302.7282

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

Pedro A. S. Salomão·Joa Weber
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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 the level set {H=s} carries a periodic orbit z of the Hamiltonian system (T^*M,\omega_0,H) representing \alpha. Examples show that the condition that {H<d} contains M is necessary and almost existence cannot be improved to everywhere existence.

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Pedro A. S. Salomão, Joa Weber. 2013-02-28. An almost existence theorem for non-contractible periodic orbits in cotangent bundles. https://doi.org/10.11606/issn.2316-9028.v6i2p385-394

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