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

  title={Ergodicity of Bowen–Margulis measure for the Benoist 3-manifolds},
  author={Harrison Bray},
  journal={Journal of Modern Dynamics},
  • Harrison Bray
  • Published 23 May 2017
  • Mathematics
  • 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… 

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