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Mat. Sb., 2008, Volume 199, Number 2, Pages 71–92 (Mi msb3663)  

This article is cited in 1 scientific paper (total in 1 paper)

On non-trivial additive cocycles on the torus

A. V. Rozhdestvenskii

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

Abstract: We construct a family of functions $f$ with zero mean on a multidimensional torus possessing a very high degree of smoothness, such that the equation
$$ w(x+\alpha)-w(x)=f(x) $$
has no measurable solutions $w$ for any badly approximable vector $\alpha$. For every vector $\alpha$ admitting an arbitrary prescribed degree of simultaneous Diophantine approximation we construct a cocycle of extremal smoothness that is asymptotically normal in the strong sense.
Bibliography: 19 titles.

DOI: https://doi.org/10.4213/sm3663

Full text: PDF file (648 kB)
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English version:
Sbornik: Mathematics, 2008, 199:2, 229–251

Bibliographic databases:

UDC: 517.518.4+517.987.5+517.983.5+519.21
MSC: Primary 37A20; Secondary 11K60
Received: 05.09.2006 and 13.09.2007

Citation: A. V. Rozhdestvenskii, “On non-trivial additive cocycles on the torus”, Mat. Sb., 199:2 (2008), 71–92; Sb. Math., 199:2 (2008), 229–251

Citation in format AMSBIB
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\paper On non-trivial additive cocycles on the torus
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\pages 229--251
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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. Goll M., Verbitskiy E., “Homoclinic Points of Principal Algebraic Actions”, Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity, Lecture Notes in Applied Mathematics and Mechanics, 3, eds. Muntean A., Rademacher J., Zagaris A., Springer Int Publishing Ag, 2016, 251–292  crossref  mathscinet  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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