Marked length spectrum of magnetized surfaces

Details Marked length spectrum of magnetized surfaces Marked length spectrum of magnetized surfaces

2005-02-20

arxiv.org/abs/math/0502424v1

Mathematics

Differential Geometry

Scientific paper

The main result presented here is that the flow associated with a riemannian metric and a non zero magnetic field on a compact oriented surface without boundary, under assumptions of hyperbolic type, cannot have the same length spectrum of topologically corresponding periodic orbits as the geodesic flow associated with another riemannian metric having a negative curvature and the same total volume. The main tool is a regularization inspired by U. Hamenst\"adt's methods.

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