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arXiv · 1407.1773

On the Conley Conjecture for Reeb Flows

Viktor L. Ginzburg·Basak Z. Gurel·Leonardo Macarini
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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.

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Viktor L. Ginzburg, Basak Z. Gurel, Leonardo Macarini. 2014-07-07. On the Conley Conjecture for Reeb Flows. https://arxiv.org/abs/1407.1773

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