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Mathematics > Differential Geometry

arXiv:1001.2677 (math)
[Submitted on 15 Jan 2010]

Title:Periodic magnetic geodesics on almost every energy level via variational methods

Authors:I.A. Taimanov
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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.
Comments: 11 pages
Subjects: Differential Geometry (math.DG); Dynamical Systems (math.DS)
Cite as: arXiv:1001.2677 [math.DG]
  (or arXiv:1001.2677v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1001.2677
Journal reference: Regular and Chaotic Dynamics 15 (2010), 598-605
Related DOI: https://doi.org/10.1134/S1560354710040131

Submission history

From: Iskander A. Taimanov [view email]
[v1] Fri, 15 Jan 2010 12:33:57 UTC (9 KB)
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