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April  2010, 4(2): 359-391. doi: 10.3934/jmd.2010.4.359

Fractal trees for irreducible automorphisms of free groups

Thierry Coulbois 1,

1. 

LATP, Université Aix-Marseille~III, Avenue de l'escadrille Normandie-Niémen, 13013 Marseille, France

Received  February 2010 Revised  June 2010 Published  August 2010

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.
Keywords: free group automorphism, Hausdorff dimension, outer space, fractal tree, directed graph construction, self-similar, IWIP., tree.
Mathematics Subject Classification: Primary: 20E05, 20E08, 37B10; Secondary: 20F65, 37C85, 57R3.
Citation: Thierry Coulbois. Fractal trees for irreducible automorphisms of free groups. Journal of Modern Dynamics, 2010, 4 (2) : 359-391. doi: 10.3934/jmd.2010.4.359
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