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arXiv · 1303.6461

On periodic orbits in cotangent bundles of non-compact manifolds

J. B. van den Berg·F. Pasquotto·T. O. Rot·R. C. A. M. Vandervorst
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Abstract

This paper is concerned with the existence of periodic orbits on energy hypersurfaces in cotangent bundles of Riemannian manifolds defined by mechanical Hamiltonians. In \cite{bpv} it was proved that, provided certain geometric assumptions are satisfied, regular mechanical hypersurfaces in $\mathbb{R}^{2n}$, in particular non-compact ones, contain periodic orbits if one homology group among the top half does not vanish. In the present paper we extend the above mentioned existence result to a class of hypersurfaces in cotangent bundles of Riemannian manifolds with flat ends.

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J. B. van den Berg, F. Pasquotto, T. O. Rot, R. C. A. M. Vandervorst. 2013-03-26. On periodic orbits in cotangent bundles of non-compact manifolds. https://arxiv.org/abs/1303.6461

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