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Matematicheskie Zametki, 2015, Volume 98, Issue 6, Pages 878–897
DOI: https://doi.org/10.4213/mzm10620 (Mi mzm10620) 		 
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
Full-text PDF (693 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm10620
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.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00360-а
12-01-33080-мол_а_вед
Received: 18.05.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 6, Pages 932–948
DOI: https://doi.org/10.1134/S0001434615110267
Bibliographic databases:
Document Type: Article
UDC: 511.43
Language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm10620
  • https://www.mathnet.ru/eng/mzm/v98/i6/p878
    • This publication is cited in the following 6 articles:
    1. A. V. Shutov, “Rauzy Fractals and their Number-Theoretic Applications”, J Math Sci, 260:2 (2022), 265  crossref
    2. A. V. Shutov, “Fraktaly Rozi i ikh teoretiko-chislovye prilozheniya”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii “Aktualnye problemy prikladnoi matematiki”. Kabardino-Balkarskaya respublika, Nalchik, Prielbruse, 22–26 maya 2018 g. Chast II, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 166, VINITI RAN, M., 2019, 110–119  mathnet  crossref
    3. A. A. Zhukova, A. V. Shutov, “n-korony v razbieniyakh tora na mnozhestva ogranichennogo ostatka”, Chebyshevskii sb., 20:3 (2019), 246–260  mathnet  crossref
    4. A. V. Shutov, “Obobschennye razbieniya Rozi i mnozhestva ogranichennogo ostatka”, Chebyshevskii sb., 20:3 (2019), 372–389  mathnet  crossref
    5. A. A. Zhukova, A. V. Shutov, “Podstanovka Rozi i lokalnaya struktura razbienii tora”, Chebyshevskii sb., 20:4 (2019), 137–157  mathnet  crossref
    6. A. V. Shutov, “Podstanovki i mnozhestva ogranichennogo ostatka”, Chebyshevskii sb., 19:2 (2018), 501–522  mathnet  crossref  mathscinet  elib
    Citing articles in Google Scholar: Russian citations, English citations
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