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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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