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

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

2011-05-30

arxiv.org/abs/1105.5965v3

Mathematics

Dynamical Systems

Scientific paper

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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