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2011 | 94 | 1 | 43-60
Tytuł artykułu

Inverse problems of symbolic dynamics

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EN
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EN
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by a substitutional system, and dynamical properties are considered as criteria for a superword being generated by an interval exchange transformation. As a consequence, one can get a morphic word appearing in an interval exchange transformation such that the frequencies of the letters are algebraic numbers of an arbitrary degree.
Concerning multidimensional systems, our main result is the following. Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word w (w = (wₙ), n ∈ ℤ) consists of a sequence of the first binary numbers of {P(n)}, i.e. wₙ = [2{P(n)}]. Denote the number of different subwords of w of length k by T(k). We prove that there exists a polynomial Q(k), depending only on the power of the polynomial P, such that T(k) = Q(k) for sufficiently large k.
Słowa kluczowe
Rocznik
Tom
94
Numer
1
Strony
43-60
Opis fizyczny
Daty
wydano
2011
Twórcy
  • Moscow Institute of Open Education, Aviatsionnyi per., 125167 Moscow, Russia
  • Shanghai University, 99 Shangda Road, BaoShan District, 200444 Shanghai, China
  • Moscow Institute of Physics and Technology, 9, Institutski per., 141700 Dolgoprudny, Moscow Region, Russia
  • Moscow State University, Leninskie Gory, 119992 Moscow, Russia
Bibliografia
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-2
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