Marked length spectrum of magnetized surfaces

Stephane Grognet (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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. Hamenstädt's methods.

Mots clés: geodesic flows; Anosov systems; magnetic fields; Lyapounoff exponents; negative curvature

Domaines: Géométrie différentielle [math.DG]

Stephane Grognet. Marked length spectrum of magnetized surfaces. 2005. ⟨hal-00004296⟩