On periodic orbits in cotangent bundles of non-compact manifolds

2013/03/26 by J. B. van den Berg, F. Pasquotto, Berg, J. B. van den +5
Mathematics · #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG

paper · pdf · doi:10.48550/arxiv.1303.6461

Revision. Accepted for publication in the Journal of Symplectic Geometry

arxiv created 2014/09/10 · arxiv updated 2014/09/11

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 \citebpv it was proved that, provided certain geometric assumptions are satisfied, regular mechanical hypersurfaces in ℝ²ⁿ, 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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