Multiplicity Of Closed Reeb Orbits On Prequantization Bundles

Abstract

We establish multiplicity results for geometrically distinct contractible closed Reeb orbits of non-degenerate contact forms on a broad class of prequantization bundles. The results hold under certain index requirements on the contact form and are sharp for unit cotangent bundles of CROSS’s. In particular, we generalize and put in the symplectic-topological context a theorem of Duan, Liu, Long and Wang for the standard contact sphere. We also prove similar results for non-hyperbolic contractible closed orbits and briefly touch upon the multiplicity problem for degenerate forms. On the combinatorial side of the question, we revisit and reprove the enhanced common jump theorem of Duan, Long and Wang, and interpret it as an index recurrence result.

Publication Date

10-1-2018

Publication Title

Israel Journal of Mathematics

Volume

228

Issue

1

Number of Pages

407-453

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11856-018-1769-y

Socpus ID

85051677348 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85051677348

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