Periodic orbits for Hamiltonian systems in cotangent bundles

Details Periodic orbits for Hamiltonian systems in cotangent bundles Periodic orbits for Hamiltonian systems in cotangent bundles

1991-11-11

arxiv.org/abs/math/9201297v1

Mathematics

Dynamical Systems

Scientific paper

We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant 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 in manifolds of negative curvature.

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