Periodic orbits of Hamiltonian flows near symplectic extrema

Viktor L. Ginzburg; Ely Kerman

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Periodic orbits of Hamiltonian flows near symplectic extrema

Viktor L. Ginzburg·Ely Kerman

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Abstract

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.

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Viktor L. Ginzburg, Ely Kerman. 2000-11-01. Periodic orbits of Hamiltonian flows near symplectic extrema. https://arxiv.org/abs/math/0011011

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