Groups of automorphisms of trees and their limit sets

Sa'ar Hersonsky, John Hubbard

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 languageEnglish
Pages (from-to)869-884
Number of pages16
JournalErgodic Theory and Dynamical Systems
Volume17
Issue number4
DOIs
StatePublished - 1 Jan 1997
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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