Periodic magnetic geodesics on almost every energy level via variational methods

Details Periodic magnetic geodesics on almost every energy level via variational methods Periodic magnetic geodesics on almost every energy level via variational methods

2010-01-15

arxiv.org/abs/1001.2677v1

Regular and Chaotic Dynamics 15 (2010), 598-605

Mathematics

Differential Geometry

11 pages

Scientific paper

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.

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