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Izv. Vyssh. Uchebn. Zaved. Mat., 2009, Number 7, Pages 3–9 (Mi ivm3040)  

This article is cited in 12 scientific papers (total in 12 papers)

One-dimensional quasiperiodic tilings admitting progressions enclosure

V. V. Krasil'shchikov, A. V. Shutov, V. G. Zhuravlev

Vladimir State Humanitarian University, Vladimir, Russia

Abstract: In this paper we consider one-dimensional quasiperiodic tilings based on the use of irrational rotations of a circle. We completely describe a wide class of progressions included in the mentioned tilings.

Keywords: one-dimensional quasiperiodic tilings, lattice enclosure.

Full text: PDF file (181 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:7, 1–6

Bibliographic databases:

UDC: 511.43
Received: 12.04.2007

Citation: V. V. Krasil'shchikov, A. V. Shutov, V. G. Zhuravlev, “One-dimensional quasiperiodic tilings admitting progressions enclosure”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 7, 3–9; Russian Math. (Iz. VUZ), 53:7 (2009), 1–6

Citation in format AMSBIB
\Bibitem{KraShuZhu09}
\by V.~V.~Krasil'shchikov, A.~V.~Shutov, V.~G.~Zhuravlev
\paper One-dimensional quasiperiodic tilings admitting progressions enclosure
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 7
\pages 3--9
\mathnet{http://mi.mathnet.ru/ivm3040}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2584200}
\zmath{https://zbmath.org/?q=an:05621435}
\elib{http://elibrary.ru/item.asp?id=12514166}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 7
\pages 1--6
\crossref{https://doi.org/10.3103/S1066369X09070019}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Krasil'shchikov, A. V. Shutov, “Description and Exact Maximum and Minimum Values of the Remainder in the Problem of the Distribution of Fractional Parts”, Math. Notes, 89:1 (2011), 59–67  mathnet  crossref  crossref  mathscinet  isi
    2. V. V. Krasil'shchikov, A. V. Shutov, “Distribution of points of one-dimensional quasilattices with respect to a variable module”, Russian Math. (Iz. VUZ), 56:3 (2012), 14–19  mathnet  crossref  mathscinet
    3. A. V. Shutov, “Trigonometricheskie summy nad odnomernymi kvazireshetkami”, Chebyshevskii sb., 13:2 (2012), 136–148  mathnet
    4. A. V. Shutov, “Mnogomernye obobscheniya summ drobnykh dolei i ikh teoretiko-chislovye prilozheniya”, Chebyshevskii sb., 14:1 (2013), 104–118  mathnet
    5. E. P. Davletyarova, A. A. Zhukova, A. V. Shutov, “Geometrization of Fibonacci numeration system and its applications to number theory”, St. Petersburg Math. J., 25:6 (2014), 893–907  mathnet  crossref  mathscinet  zmath  isi  elib
    6. V. G. Zhuravlev, “Imbedding of circular orbits and the distribution of fractional parts”, St. Petersburg Math. J., 26:6 (2015), 881–909  mathnet  crossref  mathscinet  isi  elib  elib
    7. A. V. Shutov, “Trigonometric Sums over One-Dimensional Quasilattices of Arbitrary Codimension”, Math. Notes, 97:5 (2015), 791–802  mathnet  crossref  crossref  mathscinet  isi  elib
    8. A. A. Zhukova, A. V. Shutov, “Binarnaya additivnaya zadacha s chislami spetsialnogo vida”, Chebyshevskii sb., 16:3 (2015), 246–275  mathnet  elib
    9. Kelly M., Sadun L., “Pattern Equivariant Cohomology and Theorems of Kesten and Oren”, Bull. London Math. Soc., 47:1 (2015), 13–20  crossref  mathscinet  zmath  isi
    10. A. V. Shutov, “Trigonometric Integrals over One-Dimensional Quasilattices of Arbitrary Codimension”, Math. Notes, 99:4 (2016), 590–597  mathnet  crossref  crossref  mathscinet  isi  elib
    11. E. P. Davletyarova, A. A. Zhukova, A. V. Shutov, “Geometrizatsiya obobschennykh sistem schisleniya Fibonachchi i ee prilozheniya k teorii chisel”, Chebyshevskii sb., 17:2 (2016), 88–112  mathnet  elib
    12. A. A. Zhukova, A. V. Shutov, “Geometrizatsiya sistem schisleniya”, Chebyshevskii sb., 18:4 (2017), 222–245  mathnet  crossref  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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