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Funktsional'nyi Analiz i ego Prilozheniya, 2018, Volume 52, Issue 4, Pages 23–37
DOI: https://doi.org/10.4213/faa3615 (Mi faa3615) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph

A. M. Vershikabc, P. B. Zatitskiida

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b St. Petersburg State University, Mathematics and Mechanics Faculty
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
d Saint Petersburg State University
Full-text PDF (236 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa3615
Abstract: We suggest a combinatorial classification of metric filtrations of measure spaces; a complete invariant of such a filtration is its combinatorial scheme, a measure on the space of hierarchies of the group $\mathbb Z$. In turn, the notion of a combinatorial scheme is a source of new metric invariants of automorphisms approximated by means of basic filtrations. We construct a universal graph with an adic structure such that every automorphism can be realized on its path space.
Keywords: uniform approximation, filtrations, combinatorial definiteness, universal adic graph.
Funding agency Grant number
Russian Science Foundation 17-71-20153
Received: 18.09.2018
English version:
Functional Analysis and Its Applications, 2018, Volume 52, Issue 4, Pages 258–269
DOI: https://doi.org/10.1007/s10688-018-0236-1
Bibliographic databases:
Document Type: Article
UDC: 519.1+519.2
Language: Russian
Citation: A. M. Vershik, P. B. Zatitskii, “Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph”, Funktsional. Anal. i Prilozhen., 52:4 (2018), 23–37; Funct. Anal. Appl., 52:4 (2018), 258–269
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa/v52/i4/p23
    • This publication is cited in the following 4 articles:
    1. GEORGII VEPREV, “Non-existence of a universal zero-entropy system via generic actions of almost complete growth”, Ergod. Th. Dynam. Sys., 2024, 1  crossref
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. G. Veprev, “Non-existence of a universal zero entropy system for non-periodic amenable group actions”, Isr. J. Math., 253:2 (2023), 715  crossref
    4. A. M. Vershik, P. B. Zatitskii, “On a universal Borel adic space”, J. Math. Sci. (N. Y.), 240:5 (2019), 515–524  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    References:62
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