Title

Hyperbolic Fixed Points And Periodic Orbits Of Hamiltonian Diffeomorphisms

Abstract

We prove that, for a certain class of closed monotone symplectic manifolds, any Hamiltonian diffeomorphism with a hyperbolic fixed point must necessarily have infinitely many periodic orbits. Among the manifolds in this class are complex projective spaces, some Grassmannians, and also certain product manifolds such as the product of a projective space with a symplectically aspherical manifold of low dimension. A key to the proof of this theorem is the fact that the energy required for a Floer connecting trajectory to approach an iterated hyperbolic orbit and cross its fixed neighborhood is bounded away from zero by a constant independent of the order of iteration. This result, combined with certain properties of the quantum product specific to the above class of manifolds, implies the existence of infinitely many periodic orbits. © 2014.

Publication Date

2-15-2014

Publication Title

Duke Mathematical Journal

Volume

163

Issue

3

Number of Pages

565-590

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1215/00127094-2410433

Socpus ID

84897612147 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84897612147

This document is currently not available here.

Share

COinS