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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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
Ch. Frougny and B. Solomyak, “Finite beta-expansions”,Ergodic Theory Dynamical Syst.,12, 713–723 (1992).MathSciNetGoogle Scholar
A. Bertrand-Mathis, “Developpement en base θ; repartition modulo un de la suite (xθn)n≥0; langages codes et θ-shift”,Bull. Soc. Math. France,114, 271–323 (1986).MATHMathSciNetGoogle Scholar