Transactions of the American Mathematical Society
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.
© the authors
Golé, Christophe, "Periodic Orbits for Hamiltonian Systems in Cotangent Bundles" (1994). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.