Abstract
For a 1-periodic function of finite smoothness and a Diophantine vector the solubility problem is studied for the additive cohomological equation on the torus where is the shift of the torus by the vector and is an unknown measurable function. Necessary and sufficient conditions are obtained for the conjugacy of a linear flow on the -torus to the reparametrized flow where is a positive 1-periodic function of finite smoothness.
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