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Tr. Mosk. Mat. Obs., 2015, Volume 76, Issue 2, Pages 287–308 (Mi mmo579)  

This article is cited in 7 scientific papers (total in 7 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

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

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English version:
Transactions of the Moscow Mathematical Society, 2015, 76:2, 251–269

UDC: 515.162
MSC: 57R30, 37E05, 37E25
Received: 24.01.2015
Revised: 15.03.2015

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
\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.
\jour Trans. Moscow Math. Soc.
\yr 2015
\vol 76
\issue 2
\pages 251--269

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    1. A. Ya. Maltsev, S. P. Novikov, “The theory of closed 1-forms, levels of quasiperiodic functions and transport phenomena in electron systems”, Proc. Steklov Inst. Math., 302 (2018), 279–297  mathnet  crossref  crossref  mathscinet  isi  elib
    2. W. P. Hooper, B. Weiss, “Rel leaves of the Arnoux–Yoccoz surfaces”, Sel. Math.-New Ser., 24:2 (2018), 875–934  crossref  mathscinet  zmath  isi  scopus
    3. A. Ya. Maltsev, S. P. Novikov, “Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter”, Russian Math. Surveys, 74:1 (2019), 141–173  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. R. De Leo, A. Y. Maltsev, “Quasiperiodic dynamics and magnetoresistance in normal metals”, Acta Appl. Math., 162:1 (2019), 47–61  crossref  mathscinet  zmath  isi  scopus
    5. S. P. Novikov, R. De Leo, I. A. Dynnikov, A. Ya. Maltsev, “Theory of dynamical systems and transport phenomena in normal metals”, J. Exp. Theor. Phys., 129:4, SI (2019), 710–721  crossref  mathscinet  isi  scopus
    6. A. Ya. Maltsev, “The complexity classes of angular diagrams of the metal conductivity in strong magnetic fields”, J. Exp. Theor. Phys., 129:1 (2019), 116–138  crossref  isi  scopus
    7. R. De Leo, “A survey on quasiperiodic topology”, Advanced Mathematical Methods in Biosciences and Applications, Steam-H Science Technology Engineering Agriculture Mathematics & Health, eds. F. Berezovskaya, B. Toni, Springer, 2019, 53–88  crossref  mathscinet  zmath  isi
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