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Труды Московского математического общества, 2015, том 76, выпуск 2, страницы 287–308
(Mi mmo579)
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Эта публикация цитируется в 19 научных статьях (всего в 19 статьях)
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
Аннотация:
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.
Ключевые слова и фразы:
band complex, Rips machine, Rauzy induction, measured foliation, ergodicity.
Поступила в редакцию: 24.01.2015 Исправленный вариант: 15.03.2015
Образец цитирования:
I. Dynnikov, A. Skripchenko, “Symmetric band complexes of thin type and chaotic sections which are not quite chaotic”, Тр. ММО, 76, no. 2, МЦНМО, М., 2015, 287–308; Trans. Moscow Math. Soc., 76:2 (2015), 251–269
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/mmo579 https://www.mathnet.ru/rus/mmo/v76/i2/p287
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Страница аннотации: | 344 | PDF полного текста: | 86 | Список литературы: | 74 |
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