Periodic Orbits for Hamiltonian Systems in Cotangent Bundles

Authors

Christophe Golé, Smith CollegeFollow

Document Type

Article

Publication Date

1-1-1994

Publication Title

Transactions of the American Mathematical Society

Abstract

We prove the existence of at least cl(Af) 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.

Volume

343

Issue

1

First Page

327

Last Page

347

DOI

10.1090/S0002-9947-1994-1232186-5

ISSN

00029947

Rights

© the authors

Comments

Author’s submitted manuscript.

Recommended Citation

Golé, Christophe, "Periodic Orbits for Hamiltonian Systems in Cotangent Bundles" (1994). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/84