Topological mixing of the geodesic flow on convex projective manifolds
Dynamical Systems
2021-01-28 v2 Geometric Topology
Abstract
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.
Keywords
Cite
@article{arxiv.2009.05035,
title = {Topological mixing of the geodesic flow on convex projective manifolds},
author = {Pierre-Louis Blayac},
journal= {arXiv preprint arXiv:2009.05035},
year = {2021}
}
Comments
23 pages, 5 figures. Version 2 includes new references, changes in the organisation of the paper, and the main result has been slightly enhanced