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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 297, Pages 158–164
DOI: https://doi.org/10.1134/S037196851702008X (Mi tm3840) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Combinatorics of the subshift associated with Grigorchuk's group

Rostislav Grigorchukab, Daniel Lenzc, Tatiana Nagnibedad

a Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
c Institut für Mathematik, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
d Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, Case postale 64, 1211 Geneva 4, Switzerland
Full-text PDF (185 kB) Citations (3)
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DOI: https://doi.org/10.1134/S037196851702008X
Abstract: We study combinatorial properties of the subshift induced by the substitution that describes Lysenok's presentation of Grigorchuk's group of intermediate growth by generators and relators. This subshift has recently appeared in two different contexts: on the one hand, it allowed embedding Grigorchuk's group in a topological full group, and on the other hand, it was useful in the spectral theory of Laplacians on the associated Schreier graphs.
Funding agency Grant number
Swiss National Science Foundation
National Science Foundation DMS-1207669
European Research Council AG COMPASP
The authors acknowledge support of the Swiss National Science Foundation. The first author was also supported in part by the NSF grant DMS-1207669 and by ERC AG COMPASP.
Received: February 19, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 297, Pages 138–144
DOI: https://doi.org/10.1134/S0081543817040083
Bibliographic databases:
Document Type: Article
UDC: 517.938+512.54
Language: Russian
Citation: Rostislav Grigorchuk, Daniel Lenz, Tatiana Nagnibeda, “Combinatorics of the subshift associated with Grigorchuk's group”, Order and chaos in dynamical systems, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov, Trudy Mat. Inst. Steklova, 297, MAIK Nauka/Interperiodica, Moscow, 2017, 158–164; Proc. Steklov Inst. Math., 297 (2017), 138–144
Citation in format AMSBIB
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\paper Combinatorics of the subshift associated with Grigorchuk's group
\inbook Order and chaos in dynamical systems
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 297
\pages 158--164
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://doi.org/10.1134/S037196851702008X
  • https://www.mathnet.ru/eng/tm/v297/p158
    • This publication is cited in the following 3 articles:
    1. R. Grigorchuk, S. Samarakoon, “Integrable and chaotic systems associated with fractal groups”, Entropy, 23:2 (2021), 237  crossref  mathscinet  isi
    2. D. Sell, “Combinatorics of one-dimensional simple toeplitz subshifts”, Ergod. Theory Dyn. Syst., 40:6 (2020), PII S0143385718001116, 1673–1714  crossref  mathscinet  zmath  isi  scopus
    3. Grigorchuk R., Lenz D., Nagnibeda T., “Schreier Graphs of Grigorchuk'S Group and a Subshift Associated to a Nonprimitive Substitution”, Groups, Graphs and Random Walks, London Mathematical Society Lecture Note Series, 436, eds. CeccheriniSilberstein T., Salvatori M., SavaHuss E., Cambridge Univ Press, 2017, 250–299  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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