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Journal of Modern Dynamics (JMD)
 

Fractal trees for irreducible automorphisms of free groups

Pages: 359 - 391, Issue 2, April 2010      doi:10.3934/jmd.2010.4.359

 
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Thierry Coulbois - LATP, Université Aix-Marseille~III, Avenue de l'escadrille Normandie-Niémen, 13013 Marseille, France (email)

Abstract: 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:  Hausdorff dimension, outer space, tree, free group automorphism, directed graph construction, self-similar, fractal tree, IWIP.
Mathematics Subject Classification:  Primary: 20E05, 20E08, 37B10; Secondary: 20F65, 37C85, 57R30.

Received: February 2010;      Revised: June 2010;      Available Online: August 2010.