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Mathematics > Symplectic Geometry

arXiv:1407.1773 (math)
[Submitted on 7 Jul 2014]

Title:On the Conley Conjecture for Reeb Flows

Authors: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.
Comments: 19 pages
Subjects: Symplectic Geometry (math.SG); Dynamical Systems (math.DS)
Cite as: arXiv:1407.1773 [math.SG]
  (or arXiv:1407.1773v1 [math.SG] for this version)
  https://doi.org/10.48550/arXiv.1407.1773

Submission history

From: Basak Gurel [view email]
[v1] Mon, 7 Jul 2014 17:02:27 UTC (26 KB)
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