a1 University of Helsinki, Hallituskatu 15, Helsinki, Finland
a2 The University of Bordeaux, Bordeaux, France
We produce a holomorphic familyof 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.
(Received July 10 1992)