Abstract
One presents a new variant of the theory of periodic approximations of dynamical systems and C*-algebras, namely the construction for each automorphism of the Lebesgue space of a Markov tower (or adic model) of periodic automorphisms. One gives several examples.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Literature cited
A. M. Vershik, “Uniform algebraic approximation of the shift and multiplication operators,” Dokl. Akad. Nauk SSSR,259, No. 3, 526–529 (1981).
M. Pimsner and D. Voiculescu, “Imbedding the irrational rotation C*-algebra into an AF-algebra,” J. Operator Theory,4, 201–210 (1980).
A. M. Vershik, “Countable groups which are close to finite groups,” in: F. P. Greenleaf, Invariant Means on Topological Groups [Russian translation], Mir, Moscow (1973).
A. M. Vershik, “Is the uniform algebraic approximation of the multiplication and convolution operators possible?.” J. Sov. Math.,26, No. 5 (1984).
M. A. Rieffel, “Irrational rotation of C*-algebras,” in: Internat. Congress Math., Helsinki (1978).
A. M. Vershik, “Four definitions of the scale of an automorphism,” Funkts. Anal. Prilozhen.,7, No. 3, 1–17 (1973).
A. B. Katok, Ya. G. Sinai, and A. M. Stepin, “The theory of dynamical systems and general transformation groups with invariant measure,” J. Sov. Math.,7, No. 6 (1977).
A. M. Vershik, “Multivalued mappings with invariant measure (polymorphisms) and Markov operators,” J. Sov. Math.,23, No. 3 (1983).
A. M. Vershik and O. A. Ladyzhenskaya, “The evolution of measures determined by the Navier—Stokes equations and on the solvability of the Cauchy problem for the Hopf statistical equation,” J. Sov. Math.,10, No. 2 (1978).
E. G. Effros, The Dimension Group. Preprint.
I. P. Kornfel'd, Ya. G. Sinai, and S. V. Fomin, Ergodic Theory [in Russian], Nauka, Moscow (1980).
G. Hansel and J. P. Raoult, “Ergodicity, uniformity and unique ergodicity,” Indiana Univ. Math. J.,23, No. 3, 221–237 (1973).
E. G. Effros and C. L. Shen, “Approximately finite C*-algebras and continued fractions,” Preprint.
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 115, pp. 72–82, 1982.
Rights and permissions
About this article
Cite this article
Vershik, A.M. A theorem on the Markov periodic approximation in ergodic theory. J Math Sci 28, 667–674 (1985). https://doi.org/10.1007/BF02112330
Issue Date:
DOI: https://doi.org/10.1007/BF02112330