Fractal trees for irreducible automorphisms of free groups

Details Fractal trees for irreducible automorphisms of free groups Fractal trees for irreducible automorphisms of free groups

2009-10-16

arxiv.org/abs/0910.3192v1

Mathematics

Group Theory

Scientific paper

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.

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