Numeration systems and Markov partitions from self similar tilings
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- by Brenda Praggastis
- Trans. Amer. Math. Soc. 351 (1999), 3315-3349
- DOI: https://doi.org/10.1090/S0002-9947-99-02360-0
- Published electronically: April 8, 1999
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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.References
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Bibliographic Information
- Brenda Praggastis
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- Email: praggast@sprynet.com
- Received by editor(s): October 2, 1996
- Published electronically: April 8, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 3315-3349
- MSC (1991): Primary 58F03, 34C35, 54H20
- DOI: https://doi.org/10.1090/S0002-9947-99-02360-0
- MathSciNet review: 1615950