The Conley conjecture for the cotangent bundle
Symplectic Geometry
2012-05-30 v2 Dynamical Systems
Abstract
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 proved 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.
Keywords
Cite
@article{arxiv.1006.0372,
title = {The Conley conjecture for the cotangent bundle},
author = {Doris Hein},
journal= {arXiv preprint arXiv:1006.0372},
year = {2012}
}
Comments
14 pages, 1 figure, version 2: some corrected typos and added references, one added remark on possible generalization