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Jeffrey Boland - Magnetic fields on negatively curved manifolds



JEFFREY BOLAND, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario  L8S 4K1, Canada
Magnetic fields on negatively curved manifolds


Closed 2-forms $\Omega$ on a Riemannian manifold M induce magnetic field flows in the unit tangent bundle SM which model the motion of a charged particle under the influence of the ``magnetic field'' $\Omega$. When M is negatively curved and the magnetic field is weak, these flows are hyperbolic and have many interesting properties. We discuss in particular their entropy, the regularity of their hyperbolic splitting, and the question of when they are isomorphic to (Finsler or Riemannian) geodesic flows. Particular attention will be given to the case when M is a locally symmetric space.



 

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