Bishop-Jones' Theorem and the ergodic limit set
Abstract
For a proper, Gromov-hyperbolic metric space and a discrete, non-elementary, group of isometries, we define a natural subset of the limit set at infinity of the group called the ergodic limit set. The name is motivated by the fact that every ergodic measure which is invariant for the geodesic flow on the quotient metric space is concentrated on geodesics with endpoints belonging to the ergodic limit set. We refine the classical Bishop-Jones' Theorem proving that the packing dimension of the ergodic limit set coincides with the critical exponent of the group.
Cite
@article{arxiv.2105.11774,
title = {Bishop-Jones' Theorem and the ergodic limit set},
author = {Nicola Cavallucci},
journal= {arXiv preprint arXiv:2105.11774},
year = {2024}
}
Comments
The original paper has been divided in two, according to referee's suggestion. This part contains the description of the ergodic limit set and the extension of Bishop-Jones' Theorem. This version is the one accepted for publication on Ergodic Theory and Dynamical Systems