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,
b Faculty of Mathematics, National Research University
Higher School of Economics, Moscow, Russia
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.
PDF file (416 kB)
Transactions of the Moscow Mathematical Society, 2015, 76:2, 251–269
MSC: 57R30, 37E05, 37E25
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.
\jour Trans. Moscow Math. Soc.
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