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.
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.
|Keywords:||Lagrangian systems, Negative curvature, Manifolds.|
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|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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