Bishop-Jones' Theorem and the ergodic limit set

Fuente: arXiv
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Autor principal: Cavallucci, Nicola
Formato: Preprint
Publicado: 2021
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author Cavallucci, Nicola
author_facet Cavallucci, Nicola
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2105_11774
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Bishop-Jones' Theorem and the ergodic limit set
Cavallucci, Nicola
Dynamical Systems
Metric Geometry
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.
title Bishop-Jones' Theorem and the ergodic limit set
topic Dynamical Systems
Metric Geometry
url https://arxiv.org/abs/2105.11774