# Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces.

Presented by:
D Simmons Ohio State University
Date:
Tuesday 24th June 2014 - 14:30 to 15:30
Venue:
INI Seminar Room 2
Abstract:
Let $(X,d)$ be a Gromov hyperbolic metric space, and let $\partial X$ be the Gromov boundary of $X$. Fix a group $G\leq\operatorname{Isom}(X)$ and a point $\xi\in\partial X$. We consider the Diophantine approximation of a point $\eta\in\partial X$ by points in the set $G(\xi)$. Our results generalize the work of many authors, in particular Patterson ('76) who proved most of our results in the case that $G$ is a geometrically finite Fuchsian group of the first kind and $\xi$ is a parabolic fixed point of $G$.
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