Fractal trees for irreducible automorphisms of free groups

Thierry Coulbois (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

The self-similar structure of the attracting subshift of a primitive substitution is carried over to the limit set of the repelling tree in the boundary of Outer Space of the corresponding irreducible outer automorphism of a free group. Thus, this repelling tree is self-similar (in the sense of graph directed constructions). Its Hausdorff dimension is computed. This reveals the fractal nature of the attracting tree in the boundary of Outer Space of an irreducible outer automorphism of a free group.

Mots clés: automorphism of free-group; Hausdorff dimension; real tree; fractal tree; outer space; lamination; graph directed construction; prefix-suffix automaton

Domaines: Théorie des groupes [math.GR]; Systèmes dynamiques [math.DS]

Thierry Coulbois. Fractal trees for irreducible automorphisms of free groups. 2009. ⟨hal-00424626⟩