Journal of Mathematical Sciences

, Volume 87, Issue 6, pp 4065–4066 | Cite as

On construction of a symbolic realization of hyperbolic automorphisms of the torus

  • E. A. Hirsch
Article
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Abstract

The general method of constructing an isomorphism between hyperbolic automorphisms of the torus and hyperbolic shifts, suggested by A. M. Vershik, is shown to be inapplicable to a wide class of automorphisms, namely, to those whose characteristic polynomial has at least two roots of different moduli outside the unit disk. Bibliography: 3 titles.

Keywords

Unit Disk Wide Class Characteristic Polynomial Hyperbolic Automorphism Symbolic Realization 

References

  1. 1.
    A. M. Vershik, “The arithmetic isomorphism of hyperbolic automorphisms of torus and sophic shifts”,Funct. Anal. Appl.,26, No 3, 22–27 (1992).MATHMathSciNetGoogle Scholar
  2. 2.
    Ch. Frougny and B. Solomyak, “Finite beta-expansions”,Ergodic Theory Dynamical Syst.,12, 713–723 (1992).MathSciNetGoogle Scholar
  3. 3.
    A. Bertrand-Mathis, “Developpement en base θ; repartition modulo un de la suite ( n)n≥0; langages codes et θ-shift”,Bull. Soc. Math. France,114, 271–323 (1986).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • E. A. Hirsch

There are no affiliations available

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