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.
Citation:
A. M. Vershik, “A theorem on the Markov periodic approximation in ergodic theory”, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Zap. Nauchn. Sem. LOMI, 115, "Nauka", Leningrad. Otdel., Leningrad, 1982, 72–82; J. Soviet Math., 28:5 (1985), 667–674
\Bibitem{Ver82}
\by A.~M.~Vershik
\paper A theorem on the Markov periodic approximation in ergodic theory
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~14
\serial Zap. Nauchn. Sem. LOMI
\yr 1982
\vol 115
\pages 72--82
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4041}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=660072}
\zmath{https://zbmath.org/?q=an:0505.47006}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 28
\issue 5
\pages 667--674
\crossref{https://doi.org/10.1007/BF02112330}
Linking options:
https://www.mathnet.ru/eng/znsl4041
https://www.mathnet.ru/eng/znsl/v115/p72
This publication is cited in the following 48 articles:
Mustafa İsmail Özkaraca, “Planar substitutions to Lebesgue type space-filling curves and relatively dense fractal-like sets in the plane”, Journal of Mathematical Analysis and Applications, 530:2 (2024), 127654
A. M. Vershik, G. A. Veprev, P. B. Zatitskii, “Dynamics of metrics in measure spaces and scaling entropy”, Russian Math. Surveys, 78:3 (2023), 443–499
St. Petersburg Math. J., 34:3 (2023), 313–346
A. M. Vershik, “Spektr i absolyut grafa dvustrochechnykh diagramm Yunga”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye metody. XXXIV, Zap. nauchn. sem. POMI, 517, POMI, SPb., 2022, 55–69
A. M. Vershik, “Kombinatornoe kodirovanie skhem Bernulli i asimptotika tablits Yunga”, Funkts. analiz i ego pril., 54:2 (2020), 3–24
Bezuglyi S., Karpel O., “Invariant Measures For Cantor Dynamical Systems”, Dynamics: Topology and Numbers, Contemporary Mathematics, 744, eds. Moree P., Pohl A., Snoha L., Ward T., Amer Mathematical Soc, 2020, 259–295
A. R. Minabutdinov, “Limiting Curves for the Dyadic Odometer”, J Math Sci, 247:5 (2020), 688
A. R. Minabutdinov, “Predelnye krivye dlya diadicheskogo odometra”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye i algoritmicheskie metody. XXX, Zap. nauchn. sem. POMI, 481, POMI, SPb., 2019, 74–86
Bezuglyi S. Karpel O. Kwiatkowski J., “Exact Number of Ergodic Invariant Measures For Bratteli Diagrams”, J. Math. Anal. Appl., 480:2 (2019), 123431
VALÉRIE BERTHÉ, WOLFGANG STEINER, JÖRG M. THUSWALDNER, REEM YASSAWI, “Recognizability for sequences of morphisms”, Ergod. Th. Dynam. Sys., 39:11 (2019), 2896
A. M. Vershik, P. B. Zatitskii, “Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph”, Funct. Anal. Appl., 52:4 (2018), 258–269
A. M. Vershik, P. B. Zatitskii, “On a universal Borel adic space”, J. Math. Sci. (N. Y.), 240:5 (2019), 515–524
A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333
A. M. Vershik, P. B. Zatitskii, “Universal adic approximation, invariant measures and scaled entropy”, Izv. Math., 81:4 (2017), 734–770
Dmitry Zubov, “On cohomological equations for suspension flows over Vershik automorphisms”, Mosc. Math. J., 16:2 (2016), 381–391
A. R. Minabutdinov, “Limiting curves for polynomial adic systems”, J. Math. Sci. (N. Y.), 224:2 (2017), 286–303
John C. Kieffer, 2016 IEEE International Symposium on Information Theory (ISIT), 2016, 16
Anatoly M. Vershik, “Asymptotic theory of path spaces of graded graphs and its applications”, Jpn. J. Math., 11:2 (2016), 151
A. R. Minabutdinov, “Random deviations of ergodic sums for the Pascal adic transformation in the case of the Lebesgue measure”, J. Math. Sci. (N. Y.), 209:6 (2015), 953–978
P. B. Zatitskiy, “On the possible growth rate of a scaling entropy sequence”, J. Math. Sci. (N. Y.), 215:6 (2016), 715–733
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