The Conley conjecture for the cotangent bundle

We prove the Conley conjecture for cotangent bundles of oriented, closed manifolds, and Hamiltonians which are quadratic at infinity, i.e., we show that such Hamiltonians have infinitely many periodic orbits. For the conservative systems, similar results have been proven by Lu and Mazzucchelli using...

Full description

Saved in:

Bibliographic Details
Published in:	Archiv der Mathematik Vol. 96; no. 1; pp. 85 - 100
Main Author:	Hein, Doris
Format:	Journal Article
Language:	English
Published:	Basel SP Birkhäuser Verlag Basel 2011
Subjects:	Mathematics Mathematics and Statistics 53D40 Periodic orbits Conley conjecture Floer homology 70H12 37J45
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	We prove the Conley conjecture for cotangent bundles of oriented, closed manifolds, and Hamiltonians which are quadratic at infinity, i.e., we show that such Hamiltonians have infinitely many periodic orbits. For the conservative systems, similar results have been proven by Lu and Mazzucchelli using convex Hamiltonians and Lagrangian methods. Our proof uses Floer homological methods from Ginzburg’s proof of the Conley conjecture for closed symplectically aspherical manifolds.
ISSN:	0003-889X 1420-8938
DOI:	10.1007/s00013-010-0208-z