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Entropies of magnetic flows. (Entropies des flots magnétiques.) (French) Zbl 1131.37300

Summary: A small enough magnetic field on a compact Riemannian manifold with negative curvature generates an Anosov perturbation of the geodesic flow. The topological entropy ratio is explicitly bounded. The entropy of the Liouville measure admits an Osserman-Sarnak estimate. In dimension two, for a magnetic field which is small and regular enough, and has zero mean, the flow can be parametrized by the action of the Lagrangian. The topological entropy is shown to be greater than the Liouville metric entropy, unless the magnetic field is zero and the Gauss curvature is constant; this extends a theorem of Katok known for the geodesic flow.

MSC:

37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37B40 Topological entropy
53D25 Geodesic flows in symplectic geometry and contact geometry
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References:

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