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Periodic orbits of Hamiltonian flows near symplectic critical submanifolds

Ely Kerman
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Abstract

In this paper we produce a lower bound for the number of periodic orbits of certain Hamiltonian vector fields near Bott-nondegenerate symplectic critical submanifolds. This result is then related to the problem of finding closed orbits of the motion of a charged low energy particle on a Riemannian manifold under the influence of a magnetic field

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Ely Kerman. 1999-03-18. Periodic orbits of Hamiltonian flows near symplectic critical submanifolds. https://arxiv.org/abs/math/9903100

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