References
R. Adler and B. Weiss, “Entropy a complete metric invariant for automorphisms of the torus,” Proc. Nat. Acad. Sci. U.S.A.,57, No. 6, 1573–1576 (1967).
Ya. G. Sinai, “Markov partitions and Y-diffeomorphisms,” Funkts. Anal. Prilozhen.,2, No. 1, 64–89 (1968).
R. Bowen, “Markov partitions for axiom A diffeomorphism,” Proc. Amer. Math. Soc.,92, No. 3, 725–727 (1970).
B. M. Gurevich and Ya. G. Sinai, “Toral automorphisms and Markov chains,” Addendum to the Russian translation of P. Billingsley, Ergodic Theory and Information Theory (Mir, Moscow, 1970).
E. Cawley, “Smooth Markov partitions and toral automorphisms,” Ergodic Theory Dynamical Systems,11, No. 4, 633–652 (1991).
I. P. Kornfel'd, Ya. G. Sinai and S. V. Fomin, Ergodic Theory [in Russian], Nauka, Moscow (1980).
A. M. Vershik, “The fibadic expansions of real numbers and adic transformation,” Prep. Report Inst. Mittag-Leffler, No. 4, 1–9 (1991/1992).
A. M. Vershik, “Theorem on the periodic Markov approximation in ergodic theory,” Zap. Nauch. Sem. LOMI,115, 72–82 (1982).
B. Weiss, “Subshifts of finite type and sofic systems,” Monatsh. Math.,77, 462–474 (1973).
A. N. Livshits and A. M. Vershik, “Adic models of ergodic transformations, spectral theory, and related topics,” Advances in Soviet Math., Amer. Math. Soc.,9, 185–204 (1992).
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St.-Petersburg State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 26, No. 3, pp. 22–27, July–September, 1992.
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Vershik, A.M. Arithmetic isomorphism of hyperbolic toral automorphisms and sofic shifts. Funct Anal Its Appl 26, 170–173 (1992). https://doi.org/10.1007/BF01075629
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DOI: https://doi.org/10.1007/BF01075629