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

**Simmons, D ***(Ohio State University)*

Tuesday 24 June 2014, 14:30-15:30

Seminar Room 2, Newton Institute Gatehouse

#### 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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