On the existence of periodic orbits for magnetic systems on the two-sphere
Symplectic Geometry
2015-06-16 v2 Dynamical Systems
Abstract
We prove that there exist periodic orbits on almost all compact regular energy levels of a Hamiltonian function defined on a twisted cotangent bundle over the two-sphere. As a corollary, given any Riemannian two-sphere and a magnetic field on it, there exists a closed magnetic geodesic for almost all kinetic energy levels.
Keywords
Cite
@article{arxiv.1503.09035,
title = {On the existence of periodic orbits for magnetic systems on the two-sphere},
author = {Gabriele Benedetti and Kai Zehmisch},
journal= {arXiv preprint arXiv:1503.09035},
year = {2015}
}
Comments
New title and abstract; same content; to appear in J. Mod. Dyn