Topological mixing of the geodesic flow on convex projective manifolds

Pierre-Louis Blayac

Published 2020-09-10Version 1

We introduce a natural subset of the unit tangent bundle of an irreducible convex projective manifold, which is closed and invariant under the geodesic flow, and we prove that the geodesic flow is topologically mixing on it. We also show that, for higher-rank compact convex projective manifolds, the geodesic flow is topologically mixing on each connected component of the non-wandering set.