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This article is cited in 6 scientific papers (total in 6 papers)
Exchanged Toric Tilings, Rauzy Substitution, and Bounded Remainder Sets
D. V. Kuznetsova, A. V. Shutov Vladimir State University
Abstract:
This paper is devoted to the two-dimensional problem of the distribution of the fractional parts of a linear function. A new class of tilings of the two-dimensional torus into bounded remainder sets with an effective estimate of the remainder is introduced. It is shown that examples of the tilings under consideration can be obtained by using the geometric version of the Rauzy substitution.
Keywords:
exchanged toric tiling, Rauzy substitution, bounded remainder set, distribution of the fractional parts of a linear function, fractal set, Rauzy fractal, Rauzy tiling, tribonacci sequence.
Received: 18.05.2015
Citation:
D. V. Kuznetsova, A. V. Shutov, “Exchanged Toric Tilings, Rauzy Substitution, and Bounded Remainder Sets”, Mat. Zametki, 98:6 (2015), 878–897; Math. Notes, 98:6 (2015), 932–948
Linking options:
https://www.mathnet.ru/eng/mzm10620https://doi.org/10.4213/mzm10620 https://www.mathnet.ru/eng/mzm/v98/i6/p878
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Abstract page: | 286 | Full-text PDF : | 114 | References: | 22 | First page: | 13 |
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