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Mat. Sb., 2004, Volume 195, Number 5, Pages 115–156 (Mi msb824)  

This article is cited in 4 scientific papers (total in 4 papers)

On the additive cohomological equation and time change for a linear flow on the torus with a Diophantine frequency vector

A. V. Rozhdestvenskii

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

Abstract: For a 1-periodic function $f$ of finite smoothness and a Diophantine vector $\alpha$ the solubility problem is studied for the additive cohomological equation on the torus
$$ w(T_\alpha x)-w(x)=f(x)-\int_{\mathbb T^d}f(t) dt, $$
where $T_\alpha x=x+\alpha\pmod1$ is the shift of the torus $\mathbb T^d$ by the vector $\alpha$ and $w$ is an unknown measurable function.
Necessary and sufficient conditions are obtained for the conjugacy of a linear flow on the $(d+1)$-torus to the reparametrized flow
$$ \begin{cases} \dot x=\dfrac\alpha{F(x,y)} ,
\dot y=\dfrac1{F(x,y)} , \end{cases} $$
where $F(x,y)$ is a positive 1-periodic function of finite smoothness.

DOI: https://doi.org/10.4213/sm824

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English version:
Sbornik: Mathematics, 2004, 195:5, 723–764

Bibliographic databases:

UDC: 517.9
MSC: Primary 37A30, 37A35; Secondary 46E35
Received: 05.11.2003

Citation: A. V. Rozhdestvenskii, “On the additive cohomological equation and time change for a linear flow on the torus with a Diophantine frequency vector”, Mat. Sb., 195:5 (2004), 115–156; Sb. Math., 195:5 (2004), 723–764

Citation in format AMSBIB
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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. A. V. Rozhdestvenskii, “A Sharp Estimate for the Rate of Convergence in Mean of Birkhoff Sums for Some Classes of Periodic Differentiable Functions”, Funct. Anal. Appl., 40:1 (2006), 34–41  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. V. Kozlov, “Dynamical Systems with Multivalued Integrals on a Torus”, Proc. Steklov Inst. Math., 256 (2007), 188–205  mathnet  crossref  mathscinet  zmath  elib  elib
    3. A. V. Rozhdestvenskii, “On necessary conditions for Fourier multipliers of weak type”, Izv. Math., 71:1 (2007), 75–95  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. 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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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