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

```@article{Bray2020ErgodicityOB,
title={Ergodicity of Bowen–Margulis measure for the Benoist 3-manifolds},
author={Harrison Bray},
journal={Journal of Modern Dynamics},
year={2020}
}```
• 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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