English

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

R2 v1 2026-06-21T15:30:58.757Z