Periodic magnetic geodesics on almost every energy level via variational methods
Differential Geometry
2015-05-18 v1 Dynamical Systems
Abstract
For strong exact magnetic fields the action functional (i.e., the length plus the linear magnetic term) is not bounded from below on the space of closed contractible curves and the lower estimates for critical levels are derived by using the principle of throwing out cycles. It is proved that for almost every energy level the principle of throwing out cycles gives periodic magnetic geodesics on the critical levels defined by the "thrown out" cycles.
Keywords
Cite
@article{arxiv.1001.2677,
title = {Periodic magnetic geodesics on almost every energy level via variational methods},
author = {I. A. Taimanov},
journal= {arXiv preprint arXiv:1001.2677},
year = {2015}
}
Comments
11 pages