Title

HYPERBOLIC FIXED POINTS AND PERIODIC ORBITS OF HAMILTONIAN DIFFEOMORPHISMS

Authors

Authors

V. L. Ginzburg;B. Z. Gurel

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Duke Math. J.

Keywords

SYMPLECTIC-MANIFOLDS; CONLEY CONJECTURE; FLOER HOMOLOGY; INDEX; HOMEOMORPHISMS; Mathematics

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.

Journal Title

Duke Mathematical Journal

Volume

163

Issue/Number

3

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

565

Last Page

590

WOS Identifier

WOS:000331508000004

ISSN

0012-7094

Share

COinS