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Holomorphic families of quasi-Fuchsian groups

Published online by Cambridge University Press:  19 September 2008

K. Astala  and
M. Zinsmeister
K. Astala
Affiliation:
University of Helsinki, Hallituskatu 15, Helsinki, Finland
M. Zinsmeister
Affiliation:
The University of Bordeaux, Bordeaux, France
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Abstract

We produce a holomorphic family of infinitely generated quasi-Fuchsian groups such that the Hausdorff dimension of the limit set L (Гλ) is identical to 1 for small λ, but strictly greater than 1 for λ ˜ 1. In particular, this shows that Hausdorff dimension does not depend real analytically on the parameter λ, contrary to the case of finitely generated groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 2 , June 1994 , pp. 207 - 212
Copyright
Copyright © Cambridge University Press 1994

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References

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