English

On the Conley Conjecture for Reeb Flows

Symplectic Geometry 2014-07-08 v1 Dynamical Systems

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.

Keywords

Cite

@article{arxiv.1407.1773,
  title  = {On the Conley Conjecture for Reeb Flows},
  author = {Viktor L. Ginzburg and Basak Z. Gurel and Leonardo Macarini},
  journal= {arXiv preprint arXiv:1407.1773},
  year   = {2014}
}

Comments

19 pages

R2 v1 2026-06-22T04:57:13.155Z