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


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.


Unit Disk Wide Class Characteristic Polynomial Hyperbolic Automorphism Symbolic Realization 
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  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

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  • E. A. Hirsch

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