Periodic orbits of Hamiltonian flows near symplectic extrema

Details Periodic orbits of Hamiltonian flows near symplectic extrema Periodic orbits of Hamiltonian flows near symplectic extrema

2000-11-01

arxiv.org/abs/math/0011011v1

Mathematics

Differential Geometry

19 pages, 1 figure

Scientific paper

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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