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
Copyright Status
Unknown
Socpus ID
84931572995 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84931572995
STARS Citation
Ginzburg, Viktor L.; Gürel, Başak Z.; and Macarini, Leonardo, "On The Conley Conjecture For Reeb Flows" (2015). Scopus Export 2015-2019. 122.
https://stars.library.ucf.edu/scopus2015/122