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 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.
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Acknowledgments
The author is grateful to Viktor Ginzburg for showing her this problem, helping with the solution and his kind, thoughtful advice. Furthermore, the author is very grateful to Alberto Abbondandolo, Başak Gürel and Alexandru Oancea for valuable comments.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hein, D. The Conley conjecture for the cotangent bundle. Arch. Math. 96, 85–100 (2011). https://doi.org/10.1007/s00013-010-0208-z
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DOI: https://doi.org/10.1007/s00013-010-0208-z