Patterson-Sullivan theory for coarse cocycles
Dynamical Systems
2024-08-06 v2 Differential Geometry
Geometric Topology
Abstract
In this paper we develop a theory of Patterson--Sullivan measures associated to coarse cocycles of convergence groups. This framework includes Patterson-Sullivan measures associated to the Busemann cocycle on the geodesic boundary of a Gromov hyperbolic metric spaces and Patterson-Sullivan measures on flag manifolds associated to Anosov (or more general transverse) subgroups of semisimple Lie groups, as well as more examples. Under some natural geometric assumptions on the coarse cocycle, we prove existence, uniqueness, and ergodicity results.
Cite
@article{arxiv.2404.09713,
title = {Patterson-Sullivan theory for coarse cocycles},
author = {Pierre-Louis Blayac and Richard Canary and Feng Zhu and Andrew Zimmer},
journal= {arXiv preprint arXiv:2404.09713},
year = {2024}
}
Comments
v2: 72 pages. Substantial changes to extend results to more general cocycles and Gromov products. Now ready for submission