Journal of Mathematical Sciences

, Volume 129, Issue 3, pp 3860–3867 | Cite as

Self-Similarity of Some Sequences of Points on a Circle

  • N. N. Manuylov


The self-similarity and periodicity properties are proved for the derivatives dmO0 of the sequences O0, which are obtained by shifting the unit circle by the arc \(r_2 - 1 + \sqrt 2 = [(\sqrt 2 )]\). Bibliogrhaphy: 5 titles.


Unit Circle Periodicity Property 
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    V. G. Zhuravlev, “One-dimensional Fibonacci tilings,” Izv. Ross. Akad. Nauk, Ser. Matem. (to apear)Google Scholar
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    Hyeong-Chai Jeong, Eunsang Kim, and Chang-Yeong Lee, “Noncommutative torus from Fibonacci chains via foliation,” J. Phys. A, 34, No.31, R1–R19 (2001).Google Scholar
  3. 3.
    N. N. Manuylov, “Recurrent self-similar tilings,” Chebyshev Sb., 4, No.2, 87–90 (2003).Google Scholar
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    N. N. Manuylov, “A continuous branching B-process and eigentilings of a circle,” in: Proceedings of XXV Conference of Young Scientists of Mechanics and Mathematics Faculty of MGU, MGU, Moscow (2003), pp. 121–124.Google Scholar
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    N. N. Manuylov, “Basic properties of the silver section \(1 + \sqrt 2\) and some related number sequences,” in: Collection of Papers of Young Scientists, No. 3, Vladimir (2003), pp. 168–174.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • N. N. Manuylov
    • 1
  1. 1.Vladimir State Pedagogical UniversityRussia

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