an:06568803
Zbl 1387.11052
Kuznetsova, D. V.; Shutov, A. V.
Exchanged toric tilings, Rauzy substitution, and bounded remainder sets
EN
Math. Notes 98, No. 6, 932-948 (2015); translation from Mat. Zametki 98, No. 6, 878-897 (2015).
00353029
2015
j
11J71 11H06 37B10 37B50
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
Summary: 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.