Ergodicity and equidistribution in Hilbert geometry
Ergodicity and equidistribution in Hilbert geometry
We show that dynamical and counting results characteristic of negatively curved Riemannian geometry, or more generally CAT($ -1 $) or rank-one CAT(0) spaces, also hold for rank-one properly convex projective manifolds or orbifolds, equipped with their Hilbert metrics, admitting finite Sullivan measures built from appropriate conformal densities. In particular, this …