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Numeration systems and Markov partitions from self similar tilings. (English) Zbl 0984.11008
Summary: Using self similar tilings, we represent the elements of $$\mathbb{R}^n$$ as digit expansions with digits in $$\mathbb{R}^n$$ being operated on by powers of an expansive linear map. We construct Markov partitions for hyperbolic toral automorphisms by considering a special class of self similar tilings modulo the integer lattice. We use the digit expansions inherited from these tilings to give a symbolic representation for the toral automorphisms.

##### MSC:
 11A63 Radix representation; digital problems 52C22 Tilings in $$n$$ dimensions (aspects of discrete geometry) 37B10 Symbolic dynamics 37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010)
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