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

Duration: 57 mins 45 secs

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Description:	Simmons, D (Ohio State University) Tuesday 24 June 2014, 14:30-15:30


Created:	2014-07-11 12:07
Collection:	Free Boundary Problems and Related Topics
Publisher:	Isaac Newton Institute
Copyright:	Simmons, D
Language:	eng (English)


Abstract:	Let (X,d) be a Gromov hyperbolic metric space, and let ∂X be the Gromov boundary of X. Fix a group G≤Isom(X) and a point ξ∈∂X. We consider the Diophantine approximation of a point η∈∂X by points in the set G(ξ). 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 ξ is a parabolic fixed point of G.

Abstract:

Let (X,d) be a Gromov hyperbolic metric space, and let ∂X be the Gromov boundary of X. Fix a group G≤Isom(X) and a point ξ∈∂X. We consider the Diophantine approximation of a point η∈∂X by points in the set G(ξ). 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 ξ is a parabolic fixed point of G.

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