Ergodicity of Bowen–Margulis measure for the Benoist 3-manifolds

Harrison Bray, ,Mathematical Sciences Department, George Mason University, 4400 University Dr., Fairfax, VA 22030, USA
2020 Journal of Modern Dynamics  
We study the geodesic flow of a class of 3-manifolds introduced by Benoist which have some hyperbolicity but are non-Riemannian, not CAT(0), and with non-C 1 geodesic flow. The geometries are nonstrictly convex Hilbert geometries in dimension three which admit compact quotient manifolds by discrete groups of projective transformations. We prove the Patterson-Sullivan density is canonical, with applications to counting, and construct explicitly the Bowen-Margulis measure of maximal entropy. The
more » ... ain result of this work is ergodicity of the Bowen-Margulis measure.
doi:10.3934/jmd.2020011 fatcat:cyhnhrl4azdt3boz3ofiigqz24