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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 263, Pages 72–84
(Mi tm784)
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This article is cited in 20 scientific papers (total in 20 papers)
Interval Identification Systems and Plane Sections of 3-Periodic Surfaces
I. A. Dynnikov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
Interval identification systems is a notion that, on the one hand, generalizes interval exchange transformations and, on the other hand, describes special cases of such transformations. In the present paper we overview some elementary facts, address a few questions about interval identification systems, and describe explicitly systems that allow one to construct 3-periodic surfaces in the 3-space whose intersections with planes of a fixed direction have chaotic behavior. The problem of asymptotic behavior of plane sections of 3-periodic surfaces was posed by S. P. Novikov in 1982 and studied then by his students. One of the most interesting remaining open questions about such sections is reduced to the study of interval identification systems.
Received in April 2008
Citation:
I. A. Dynnikov, “Interval Identification Systems and Plane Sections of 3-Periodic Surfaces”, Geometry, topology, and mathematical physics. I, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 263, MAIK Nauka/Interperiodica, Moscow, 2008, 72–84; Proc. Steklov Inst. Math., 263 (2008), 65–77
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https://www.mathnet.ru/eng/tm784 https://www.mathnet.ru/eng/tm/v263/p72
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Abstract page: | 467 | Full-text PDF : | 173 | References: | 68 | First page: | 15 |
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