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Smooth cocycles for an irrational rotation. (English) Zbl 0769.28013

Summary: Explicit examples of smooth cocycles not cohomologous to constants are constructed. Necessary and sufficient conditions on the irrational number \(\theta\) are given for the existence of such cocycles. It is shown that, depending on \(\theta\), the set of \(C^ r\) cocycles whose skew-product is ergodic is either residual or empty.

MSC:

28D05 Measure-preserving transformations
28D15 General groups of measure-preserving transformations
11K50 Metric theory of continued fractions
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References:

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