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Trudy Moskovskogo Matematicheskogo Obshchestva, 2015, Volume 76, Issue 2, Pages 287–308 (Mi mmo579)  
This article is cited in 19 scientific papers (total in 19 papers)

Symmetric band complexes of thin type and chaotic sections which are not quite chaotic

I. Dynnikova, A. Skripchenkob

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Faculty of Mathematics, National Research University Higher School of Economics, Moscow, Russia
Full-text PDF (416 kB) Citations (19)
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Abstract: In a recent paper we constructed a family of foliated 2-complexes of thin type whose typical leaves have two topological ends. Here we present simpler examples of such complexes that are, in addition, symmetric with respect to an involution and have the smallest possible rank. This allows for constructing a 3-periodic surface in the three-space with a plane direction such that the surface has a central symmetry, and the plane sections of the chosen direction are chaotic and consist of infinitely many connected components. Moreover, typical connected components of the sections have an asymptotic direction, which is due to the fact that the corresponding foliation on the surface in the 3-torus is not uniquely ergodic.
References: 25 entries.
Key words and phrases: band complex, Rips machine, Rauzy induction, measured foliation, ergodicity.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12469
Dynasty Foundation
Received: 24.01.2015
Revised: 15.03.2015
English version:
Transactions of the Moscow Mathematical Society, 2015, Volume 76, Issue 2, Pages 251–269
DOI: https://doi.org/10.1090/mosc/246
Bibliographic databases:
Document Type: Article
UDC: 515.162
MSC: 57R30, 37E05, 37E25
Language: English
Citation: I. Dynnikov, A. Skripchenko, “Symmetric band complexes of thin type and chaotic sections which are not quite chaotic”, Tr. Mosk. Mat. Obs., 76, no. 2, MCCME, M., 2015, 287–308; Trans. Moscow Math. Soc., 76:2 (2015), 251–269
Citation in format AMSBIB
\Bibitem{DynSkr15}
\by I.~Dynnikov, A.~Skripchenko
\paper Symmetric band complexes of thin type and chaotic sections which are not quite chaotic
\serial Tr. Mosk. Mat. Obs.
\yr 2015
\vol 76
\issue 2
\pages 287--308
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo579}
\elib{https://elibrary.ru/item.asp?id=24850147}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2015
\vol 76
\issue 2
\pages 251--269
\crossref{https://doi.org/10.1090/mosc/246}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960081631}
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    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Trudy Moskovskogo Matematicheskogo Obshchestva
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