Periodic orbits of Hamiltonian flows near symplectic extrema

Viktor L. Ginzburg and Ely Kerman

Vol. 206 (2002), No. 1, 69–91

DOI: 10.2140/pjm.2002.206.69

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.

Milestones

Received: 17 December 2000

Published: 1 September 2002