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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Numeration systems and Markov partitions
from self similar tilings


Author: Brenda Praggastis
Journal: Trans. Amer. Math. Soc. 351 (1999), 3315-3349
MSC (1991): Primary 58F03, 34C35, 54H20
Published electronically: April 8, 1999
MathSciNet review: 1615950
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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.


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Additional Information

Brenda Praggastis
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: praggast@sprynet.com

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02360-0
PII: S 0002-9947(99)02360-0
Received by editor(s): October 2, 1996
Published electronically: April 8, 1999
Article copyright: © Copyright 1999 American Mathematical Society