arXiv:1711.03535 Abstract | arXiv Analytics

arXiv:1711.03535 [math.DS]Abstract References Reviews Resources

Tree substitutions and Rauzy fractals

Published 2017-11-08Version 1

We work with attracting subshifts generated by substitutions which are also irreducible parageometric automorphisms of free groups. For such a dynamical system, we construct a tree substitution to approximate the repelling real tree of the automorphism. We produce images of this tree inside the Rauzy fractal when the substitution is irreducible Pisot. We describe the contour of this tree and compute an interval exchange transformation of the circle covering the original substitution.

Comments: 44 pages, 20 figures

Categories: math.DS, math.GR

Subjects: 20E05, 20E08, 20F65, 28A80, 37B10, 37E05, 52C23

Keywords: rauzy fractal, tree substitution, interval exchange transformation, original substitution, tree inside

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