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

Peyerimhoff, N.; Siburg, K.F.

Authors

K.F. Siburg



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.

Citation

Peyerimhoff, N., & Siburg, K. (2003). The dynamics of magnetic flows for energies above Mane's critical value. Israel Journal of Mathematics, 135, 269-298

Journal Article Type Article
Online Publication Date Jan 1, 2003
Publication Date Jan 1, 2003
Deposit Date May 1, 2007
Journal Israel Journal of Mathematics
Print ISSN 0021-2172
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 135
Pages 269-298
Keywords Lagrangian systems, Negative curvature, Manifolds.
Publisher URL http://www.ma.huji.ac.il/~ijmath/

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