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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 403, Pages 95–102
(Mi znsl5250)
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This article is cited in 4 scientific papers (total in 4 papers)
A realization of the Pascal automorphism in the concatenation graph, and the function $s_2(n)$
A. A. Lodkin, I. E. Manaev, A. R. Minabutdinov St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia
Abstract:
A class of concatenation dynamical systems is introduced. Various automorphisms, including the Morse and Pascal automorphisms, can be regarded as automorphisms of this class. In this realization, a natural number-theoretic interpretation of the problem whether the spectrum of an automorphism is discrete arises. In particular, the known character of the asymptotic behavior of the function $s_2(n)$ allows one to immediately see the nondiscreteness of the spectrum of the Morse automorphism and to give a new formulation of the discreteness problem in the case of the Pascal automorphism.
Key words and phrases:
concatenation graph, adic automorphism, Pascal automorphism, Morse automorphism, sum-of-digits function, discrete spectrum.
Received: 15.10.2012
Citation:
A. A. Lodkin, I. E. Manaev, A. R. Minabutdinov, “A realization of the Pascal automorphism in the concatenation graph, and the function $s_2(n)$”, Representation theory, dynamical systems, combinatorial methods. Part XXI, Zap. Nauchn. Sem. POMI, 403, POMI, St. Petersburg, 2012, 95–102; J. Math. Sci. (N. Y.), 190:3 (2013), 459–463
Linking options:
https://www.mathnet.ru/eng/znsl5250 https://www.mathnet.ru/eng/znsl/v403/p95
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Abstract page: | 225 | Full-text PDF : | 67 | References: | 29 |
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