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 Mat. Zametki, 1995, Volume 58, Issue 3, Pages 394–410 (Mi mz2056)

Distribution of values of linear functions and asymptotic behavior of trajectories of some dynamical systems

N. G. Moshchevitin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The asymptotic behavior of mean values for integrals of quasiperiodic functions, which characterizes the uniformity of the distribution of irrational windings on a torus, is shown to be essentially dependent on the dimension of the torus. We prove the nonrecurrence of mean values for arbitrarily smooth three-frequency quasiperiodic functions. We also present a series of results concerning the distribution of fractional parts for systems of linear functions.

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English version:
Mathematical Notes, 1995, 58:3, 948–959

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Citation: N. G. Moshchevitin, “Distribution of values of linear functions and asymptotic behavior of trajectories of some dynamical systems”, Mat. Zametki, 58:3 (1995), 394–410; Math. Notes, 58:3 (1995), 948–959

Citation in format AMSBIB
\Bibitem{Mos95} \by N.~G.~Moshchevitin \paper Distribution of values of linear functions and asymptotic behavior of trajectories of some dynamical systems \jour Mat. Zametki \yr 1995 \vol 58 \issue 3 \pages 394--410 \mathnet{http://mi.mathnet.ru/mz2056} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1368548} \zmath{https://zbmath.org/?q=an:0857.11037} \transl \jour Math. Notes \yr 1995 \vol 58 \issue 3 \pages 948--959 \crossref{https://doi.org/10.1007/BF02304772} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TW84800008} 

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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. N. G. Moshchevitin, “Recurrence of the integral of a smooth three-frequency conditionally periodic function”, Math. Notes, 58:5 (1995), 1187–1196
2. S. V. Konyagin, “Recurrence of the integral of an odd conditionally periodic function”, Math. Notes, 61:4 (1997), 473–479
3. N. G. Moshchevitin, “Differential equations with almost periodic or conditionally periodic coefficients: Recurrence and reducibility”, Math. Notes, 64:2 (1998), 194–201
4. E. V. Kolomeikina, N. G. Moshchevitin, “Nonrecurrence in Mean of Sums along the Kronecker Sequence”, Math. Notes, 73:1 (2003), 132–135
5. A. V. Rozhdestvenskii, “An Additive Cohomological Equation and Typical Behavior of Birkhoff Sums over a Translation of the Multidimensional Torus”, Proc. Steklov Inst. Math., 256 (2007), 263–274
6. A. V. Rozhdestvenskii, “On non-trivial additive cocycles on the torus”, Sb. Math., 199:2 (2008), 229–251
7. N. G. Moshchevitin, “Khintchine's singular Diophantine systems and their applications”, Russian Math. Surveys, 65:3 (2010), 433–511
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