Topological mixing of the geodesic flow on convex projective manifolds

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