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Limit sets of free groups, Hausdorff dimension and subshifts of finite type
by
Shmuel Friedland
University of Illinois at Chicago
Let F be a free Kleinian group on r generators. It is well known that F can be described as an inifinite 2r regular tree T and its limit set \Lambda(F) = \partialT can be given by the appropriate subshift of finite type on 2r generators. One can put the standard graph metric on T which induces a Cantorian metric on \partialT or the hyperbolic metric on T which induces the standard metric on \Lambda(F) contained in S2. We then discuss the notion of the Hausdorff dimension of the limit set and the critical exponent of the corresponding Poincaré series with respect to the two metrics. In particular we shall give a simple lower bound for the classical critical exponent of the Poincaré series.
Date received: January 11, 1996
Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caab-76.