On the rigidity of magnetic systems with the same magnetic geodesics-Reference-Cited by-同舟云学术

On the rigidity of magnetic systems with the same magnetic geodesics

Published:2005-09-20 Issue:2 Volume:134 Page:427-434
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Burns Keith,Matveev Vladimir

Abstract

We study the analogue for magnetic flows of the classical question of when two different metrics on the same manifold share geodesics, which are the same up to reparametrization.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2006-134-02/S0002-9939-05-08196-7/S0002-9939-05-08196-7.pdf

Reference21 articles.

1. E. Beltrami, Resoluzione del problema: riportari i punti di una superficie sopra un piano in modo che le linee geodetische vengano rappresentante da linee rette, Ann. Mat. 1 (1865), no. 7.

2. Anosov magnetic flows, critical values and topological entropy;Burns, Keith;Nonlinearity,2002

3. Magnetic flows of Anosov type;Gouda, Norio;Tohoku Math. J. (2),1997

4. Flots magnétiques en courbure négative;Grognet, Stéphane;Ergodic Theory Dynam. Systems,1999

5. Entropies des flots magnétiques;Grognet, Stéphane;Ann. Inst. H. Poincar\'{e} Phys. Th\'{e}or.,1999

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Integrable magnetic geodesic flows on 2-surfaces ^*;Nonlinearity;2023-03-15

2. Periodic magnetic geodesics on Heisenberg manifolds;Annals of Global Analysis and Geometry;2021-07-19

3. On First Integrals of Two-Dimensional Geodesic Flows;Siberian Mathematical Journal;2020-07

4. Integrable Magnetic Flows on the Two-Torus: Zoll Examples and Systolic Inequalities;The Journal of Geometric Analysis;2020-02-25

5. Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs;Communications in Mathematical Physics;2017-01-06