Exchanged toric tilings, Rauzy substitution, and bounded remainder sets

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• 作者：D. V. Kuznetsova ; A. V. Shutov
• 关键词：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
• 刊名：Mathematical Notes
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：98
• 期：5-6
• 页码：932-948
• 全文大小：754 KB
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• 作者单位：D. V. Kuznetsova (1)
  A. V. Shutov (1)
  
  1. Stoletovs Vladimir State University, Vladimir, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876

文摘

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