Abstract
Let T be a locally finite simplicial tree and let Γ ⊂ Aut(T) be a finitely generated discrete subgroup. We obtain an explicit formula for the critical exponent of the Poincaré series associated with Γ, which is also the Hausdorff dimension of the limit set of Γ; this uses a description due to Lubotzky of an appropriate fundamental domain for finite index torsion-free subgroups of Γ. 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 the space of deformations of Γ.
Original language | English |
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Pages (from-to) | 869-884 |
Number of pages | 16 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 17 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jan 1997 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics