Baggett, L.; Merrill, K. Smooth cocycles for an irrational rotation. (English) Zbl 0769.28013 Isr. J. Math. 79, No. 2-3, 281-288 (1992). 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. Cited in 1 ReviewCited in 6 Documents MSC: 28D05 Measure-preserving transformations 28D15 General groups of measure-preserving transformations 11K50 Metric theory of continued fractions Keywords:ergodic skew-product; irrational rotation; smooth cocycles not cohomologous to constants PDFBibTeX XMLCite \textit{L. Baggett} and \textit{K. Merrill}, Isr. J. Math. 79, No. 2--3, 281--288 (1992; Zbl 0769.28013) Full Text: DOI References: [1] A. Ya. Khinchin,Continued Fractions, University of Chicago Press, 1964. · Zbl 0117.28601 [2] L. Kuipers and H. Niederreiter,Uniform Distribution of Sequences, Wiley, 1974. · Zbl 0281.10001 [3] Krygin, A., Examples of Ergodic Cylindrical Cascades, Math. Notes U.S.S.R., 16, 1180-1186 (1974) · Zbl 0318.54042 · doi:10.1007/BF01098447 [4] Nerurkar, M., On the Construction fo Smooth Ergodic Skew-Prodicts, Ergod. Th. and Dynam. Sys., 8, 311-326 (1988) · Zbl 0662.58028 · doi:10.1017/S0143385700004454 [5] K. Schmidt,Cocycles of Ergodic Transformation Groups, Lecture Notes in Mathematics Vol. 1, Mac Millan Co. of India, 1977. · Zbl 0421.28017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.