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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Periodic orbits for Hamiltonian systems in cotangent bundles
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by Christophe Golé PDF
Trans. Amer. Math. Soc. 343 (1994), 327-347 Request permission

Abstract:

We prove the existence of at least $\operatorname {cl}(M)$ periodic orbits for certain time-dependent Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold M. These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on M. We discretize the variational problem by decomposing the time-1 map into a product of "symplectic twist maps". A second theorem deals with homotopically non-trivial orbits of negative curvature.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 327-347
  • MSC: Primary 58E05; Secondary 34C25, 58F05, 58F22
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1232186-5
  • MathSciNet review: 1232186