Numeration systems and Markov partitions from self similar tilings

Praggastis, Brenda

doi:10.1090/S0002-9947-99-02360-0

Numeration systems and Markov partitions from self similar tilings
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Trans. Amer. Math. Soc. 351 (1999), 3315-3349 Request permission

Abstract:

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.

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