Geodesic
On non-trivial additive cocycles on the torus
Sbornik. Mathematics, Tome 199 (2008) no. 2, pp. 229-251 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. V. Rozhdestvenskii. On non-trivial additive cocycles on the torus. Sbornik. Mathematics, Tome 199 (2008) no. 2, pp. 229-251. http://geodesic.mathdoc.fr/item/SM_2008_199_2_a3/

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