Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems

Bahri, Abbas; Taimanov, Iskander

doi:10.1090/S0002-9947-98-02108-4

Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems
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by Abbas Bahri and Iskander A. Taimanov PDF

Trans. Amer. Math. Soc. 350 (1998), 2697-2717 Request permission

Abstract:

A Lagrangian system describing a motion of a charged particle on a Riemannian manifold is studied. For this flow an analog of a Ricci curvature is introduced, and for Ricci positively curved flows the existence of periodic orbits is proved.

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