On the existence of infinitely many invariant Reeb orbits
Symplectic Geometry
2014-11-20 v2
Abstract
In this article we extend results of Grove and Tanaka on the existence of isometry-invariant geodesics to the setting of Reeb flows and strict contactomorphisms. Specifically, we prove that if M is a closed connected manifold with the property that the Betti numbers of the free loop space are asymptotically unbounded then for every fibrewise star-shaped hypersurface in the cotangent bundle of M and every strict contactomorphism of that hypersurface which is contact-isotopic to the identity, there are infinitely many invariant Reeb orbits.
Keywords
Cite
@article{arxiv.1411.4847,
title = {On the existence of infinitely many invariant Reeb orbits},
author = {Will J. Merry and Kathrin Naef},
journal= {arXiv preprint arXiv:1411.4847},
year = {2014}
}
Comments
49 pages; Version 2 - added reference to Lu's work arxiv:1411.3209