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arXiv · 1411.4847

On the existence of infinitely many invariant Reeb orbits

Will J. Merry·Kathrin Naef
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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.

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Will J. Merry, Kathrin Naef. 2014-11-18. On the existence of infinitely many invariant Reeb orbits. https://arxiv.org/abs/1411.4847

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