GROUPS OF AUTOMORPHISMS OF TREES AND THEIR LIMIT-SETS

Let T be a locally finite simplicial tree and let Gamma subset of Aut( T) be a finitely generated discrete subgroup. We obtain an explicit fo rmula for the critical exponent of the Poincare series associated with Gamma, which is also the Hausdorff dimension of the limit set of Gamm a; this uses a description due to Lubotzky of an appropriate fundament al domain for finite index torsion-free subgroups of Gamma. Coornaert, generalizing work of Sullivan, showed that the limit set is of finite positive measure in its dimension; we give a new proof of this result . Finally, we show that the critical exponent is locally constant on t he space of deformations of Gamma.