On the Conley Conjecture for Reeb Flows

Abstract

In this paper we prove the existence of infinitely many closed Reeb orbits for a certain class of contact manifolds. This result can be viewed as a contact analogue of the Hamiltonian Conley conjecture. The manifolds for which the contact Conley conjecture is established are the pre-quantization circle bundles with aspherical base. As an application, we prove that for a surface of genus at least two with a non-vanishing magnetic field, the twisted geodesic flow has infinitely many periodic orbits on every low energy level.

arXiv comment19 pages

References in corpus (5)

• Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level
• Contact homology of good toric contact manifolds
• Vanishing of the contact homology of overtwisted contact 3--manifolds
• Symplectically degenerate maxima via generating functions
• Perfect Reeb flows and action-index relations

Cited by in corpus (2)

• Infinitely many periodic orbits in non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level
• My Contact Homology Shopping List