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A criterion for the failure of Ruelle's property

Published online by Cambridge University Press:  14 November 2006

CHRISTOPHER J. BISHOP
CHRISTOPHER J. BISHOP
Affiliation:
Mathematics Department, SUNY at Stony Brook, Stony Brook, NY 11794-3651, USA (e-mail: bishop@math.sunysb.edu)
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Abstract

Ruelle proved that for quasiconformal deformations of cocompact Fuchsian groups, the Hausdorff dimension of the limit set is an analytic function of the deformation. In this paper, we give a criterion for the failure of analyticity for certain infinitely generated groups. In particular, we show that it fails for any infinite abelian cover of a compact surface, answering a question of Astala and Zinsmeister.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 6 , December 2006 , pp. 1733 - 1748
Copyright
2006 Cambridge University Press

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