Ergodic Theory and Dynamical Systems

Research Article

Holomorphic families of quasi-Fuchsian groups

K. Astalaa1 and M. Zinsmeistera2

a1 University of Helsinki, Hallituskatu 15, Helsinki, Finland

a2 The University of Bordeaux, Bordeaux, France

Abstract

We produce a holomorphic family of infinitely generated quasi-Fuchsian groups such that the Hausdorff dimension of the limit set Lλ) 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.

(Received July 10 1992)