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:
magnetic geodesics, closed extremals, calculus of variations in the large
Citation:
Taimanov I. A., Periodic magnetic geodesics on almost every energy level via variational methods, Regular and Chaotic Dynamics,
2010, Volume 15, Numbers 4-5,
pp. 598-605