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

This article is cited in 7 scientific papers (total in 7 papers)

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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Received: 08.08.1994

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
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\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
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\transl
\jour Math. Notes
\yr 1995
\vol 58
\issue 3
\pages 948--959
\crossref{https://doi.org/10.1007/BF02304772}
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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  mathscinet  zmath  isi
    2. S. V. Konyagin, “Recurrence of the integral of an odd conditionally periodic function”, Math. Notes, 61:4 (1997), 473–479  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. N. G. Moshchevitin, “Differential equations with almost periodic or conditionally periodic coefficients: Recurrence and reducibility”, Math. Notes, 64:2 (1998), 194–201  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. E. V. Kolomeikina, N. G. Moshchevitin, “Nonrecurrence in Mean of Sums along the Kronecker Sequence”, Math. Notes, 73:1 (2003), 132–135  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  zmath  elib  elib
    6. A. V. Rozhdestvenskii, “On non-trivial additive cocycles on the torus”, Sb. Math., 199:2 (2008), 229–251  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. N. G. Moshchevitin, “Khintchine's singular Diophantine systems and their applications”, Russian Math. Surveys, 65:3 (2010), 433–511  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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