## Institute for Mathematical Sciences

## Preprint ims91-21

** C. Gole**
* Periodic Orbits for Hamiltonian systems in Cotangent Bundles*

Abstract: 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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