Ergodicity and equidistribution in strictly convex Hilbert geometry
Dynamical Systems
2021-04-29 v3 Group Theory
Geometric Topology
Abstract
In this paper 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 geometrically-finite strictly convex projective structures equipped with their Hilbert metric. More specifically, such structures admit a finite Sullivan measure; with respect to this measure, the Hilbert geodesic flow is strongly mixing, and orbits and primitive closed geodesics equidistribute, allowing us to asymptotically enumerate these objects.
Cite
@article{arxiv.2008.00328,
title = {Ergodicity and equidistribution in strictly convex Hilbert geometry},
author = {Feng Zhu},
journal= {arXiv preprint arXiv:2008.00328},
year = {2021}
}
Comments
32 pages. Title edited to more accurately reflect scope of results; minor changes to formatting and terminology; typos corrected