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Sbornik: Mathematics, 2008, Volume 199, Issue 2, Pages 229–251
DOI: https://doi.org/10.1070/SM2008v199n02ABEH003917 (Mi sm3663) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On non-trivial additive cocycles on the torus

A. V. Rozhdestvenskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (400 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2008v199n02ABEH003917
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.
Received: 05.09.2006 and 13.09.2007
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 2, Pages 71–92
DOI: https://doi.org/10.4213/sm3663
Bibliographic databases:
UDC: 517.518.4+517.987.5+517.983.5+519.21
MSC: Primary 37A20; Secondary 11K60
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 2 articles:
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    English version PDF:22
    References:65
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