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The dynamics of magnetic flows for energies above Mane's critical value.

Peyerimhoff, N. and Siburg, K. F. (2003) 'The dynamics of magnetic flows for energies above Mane's critical value.', Israel journal of mathematics., 135 . pp. 269-298.

Abstract

We show that, for energies above Mane's critical value, minimal magnetic geodesics are Riemannian (A,0)-quasi-geodesics where A -> 1 as the energy tends to infinity. As a consequence, on negatively curved manifolds, minimal magnetic geodesics lie in tubes around Riemannian geodesics. Finally, we investigate a natural metric introduced by Mane via the so-called action potential. Although this magnetic metric does depend on the magnetic field, the associated magnetic length turns out to be just the Riemannian length.

Item Type:Article
Additional Information:
Keywords:Lagrangian systems, Negative curvature, Manifolds.
Full text:Full text not available from this repository.
Publisher Web site:http://www.ma.huji.ac.il/~ijmath/
Record Created:01 May 2007
Last Modified:08 Apr 2009 16:30

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