Periodic orbits of Hamiltonian flows near symplectic extrema

Viktor L. Ginzburg; Ely Kerman

Periodic orbits of Hamiltonian flows near symplectic extrema

Differential Geometry 2007-05-23 v1 Dynamical Systems Symplectic Geometry

Authors: Viktor L. Ginzburg , Ely Kerman

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.

Keywords

Hamiltonian flows periodic orbits symplectic extrema Bott-nondegenerate level sets magnetic field

Cite

@article{arxiv.math/0011011,
  title  = {Periodic orbits of Hamiltonian flows near symplectic extrema},
  author = {Viktor L. Ginzburg and Ely Kerman},
  journal= {arXiv preprint arXiv:math/0011011},
  year   = {2007}
}