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Arithmetic construction of sofic partitions of hyperbolic toral automorphisms

Published online by Cambridge University Press:  01 April 1998

RICHARD KENYON  and
ANATOLY VERSHIK
RICHARD KENYON
Affiliation:
CNRS UMR 128, Ecole Normale Supérieure de Lyon, 46, allée d'Italie, 69364 Lyon, France Laboratoire de Topologie, Bât 425, Université Paris-Sud, 91405 Orsay, France.
ANATOLY VERSHIK
Affiliation:
St. Petersburg Branch of Mathematical Institute of the Russian Acad. Sciences, 27 Fontanka, 191011 St. Petersburg, Russia
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Abstract

For each irreducible hyperbolic automorphism $A$ of the $n$-torus we construct a sofic system $(\Sigma,\sigma)$ and a bounded-to-one continuous semiconjugacy from $(\Sigma,\sigma)$ to $({\Bbb T}^n,A)$. This construction is natural in the sense that it depends only on the characteristic polynomial of $A$ and, furthermore, it has an arithmetic interpretation.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 2 , April 1998 , pp. 357 - 372
Copyright
1998 Cambridge University Press

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