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Stepped surfaces and Rauzy fractals induced from automorphisms on the free group of rank 2

2011/05/30 by Hiromi Ei, Ei, Hiromi
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1105.5965

arxiv created 2011/11/09 · arxiv updated 2011/11/10

Abstract

For substitution satisfying Pisot, irreducible, unimodular condition, a tiling substitution plays a key role in construction of a stepped surface and Rauzy fractal. In this paper we will extend the method to hyperbolic automorphisms on the free group of rank 2 in some class, and obtain set equations of Rauzy fractals by virtue of a tiling substitution. We will also see that the domain exchange transformation on Rauzy fractal is just a two interval exchange transformation.

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