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

DOI:
https://doi.org/10.1090/S0002-9947-99-02360-0

Published electronically:
April 8, 1999

MathSciNet review:
1615950

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Using self similar tilings we represent the elements of as digit expansions with digits in 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:
https://doi.org/10.1090/S0002-9947-99-02360-0

Received by editor(s):
October 2, 1996

Published electronically:
April 8, 1999

Article copyright:
© Copyright 1999
American Mathematical Society