Periodic orbits of Hamiltonian flows near symplectic extrema

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For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a nondegenerate (i.e. symplectic) magnetic field has periodic orbits on a sequence of energy levels converging to zero.
19 pages, 1 figure

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Differential Geometry, Dynamical Systems, Symplectic Geometry, 58F05(primary), 58F22(secondary)

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https://dspace.dare.co.zw/handle/123456789/94447

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arXiv

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