On The Conley Conjecture For Reeb Flows

Keywords

Conley conjecture; contact and Floer homology; contact forms and Reeb flows; Periodic orbits; twisted geodesic 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.

Publication Date

6-17-2015

Publication Title

International Journal of Mathematics

Volume

26

Issue

7

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1142/S0129167X15500470

Socpus ID

84931572995 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84931572995

This document is currently not available here.

Share

COinS