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arXiv · 1811.09213

The Omega limit set of a family of chords

Edward Belbruno·Urs Frauenfelder·Otto van Koert
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Abstract

In this paper we study the limit behavior of a family of chords on compact energy hypersurfaces of a family of Hamiltonians. Under the assumption that the energy hypersurfaces are all of contact type, we give results on the Omega limit set of this family of chords. Roughly speaking, such a family must either end in a degeneracy, in which case it joins another family, or can be continued. This gives a Floer theoretic explanation of the behavior of certain families of symmetric periodic orbits in many well-known problems, including the restricted three-body problem.

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Edward Belbruno, Urs Frauenfelder, Otto van Koert. 2018-11-22. The Omega limit set of a family of chords. https://arxiv.org/abs/1811.09213

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