The Conley conjecture for the cotangent bundle

Details The Conley conjecture for the cotangent bundle The Conley conjecture for the cotangent bundle

2010-06-02

arxiv.org/abs/1006.0372v2

Mathematics

Symplectic Geometry

14 pages, 1 figure, version 2: some corrected typos and added references, one added remark on possible generalization

Scientific paper

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.

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