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The infinite word problem and limit sets in Fuchsian groups

Published online by Cambridge University Press:  19 September 2008

Caroline Series
Caroline Series
Affiliation:
Mathematics Institute, University of Warwick, Coventry CVA 1AL, England
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Abstract

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Let Г be a finitely generated non-elementary Fuchsian group acting in the disk. With the exception of a small number of co-compact Г, we give a representation of g ∈ Г as a product of a fixed set of generators Гo in a unique shortest ‘admissible form’. Words in this form satisfy rules which after a suitable coding are of finite type. The space of infinite sequences Σ of generators satisfying the same rules is identified in a natural way with the limit set Λ of Г by a map which is bijective except at a countable number of points where it is two to one. We use the theory of Gibbs measures onΣ to construct the so-called Patterson measure on Λ [8], [9]. This measure is, in fact, Hausdorff 5-dimensional measure on Λ, where S is the exponent of convergence of Г.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 3 , September 1981 , pp. 337 - 360
Copyright
Copyright © Cambridge University Press 1981

References

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