Entropy collapse versus entropy rigidity for Reeb and Finsler flows

Abstract: The topological entropy of a flow on a compact manifold is a measure of complexity related to many other notions of growth. By celebrated works of Katok and Besson-Courtois-Gallot, the topological entropy of geodesic flows of Riemannian metrics with a fixed volume on a manifold M that carries a metric of negative curvature is uniformly bounded from below by a positive constant depending only on M. We show that this result persists for all (possibly irreversible) Finsler flows, but that on every closed contact manifold there exists a Reeb flow of fixed volume and arbitrarily small entropy. This is joint work with Alberto Abbondandolo, Murat Saglam and Felix Schlenk.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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