Svetic, R. E. A function with locally uncountable rotation set. (English) Zbl 0963.28013 Acta Math. Hung. 81, No. 4, 305-314 (1998). Summary: The rotain set \(\Gamma\) of a Lebesgue measurable real valued function on the circle is the set of \(\alpha \in \mathbb R\) for wich \(\frac 1{n+1}\sum^n_{k=0}f(x+k\alpha)\) converges as \(n\to \infty\) for almost every \(x\). Z. Buczolich [Ergodic Theory Dyn. Syst. 16, No. 6, 1185-1196 (1996; Zbl 0869.28008)] has constructed a non-integrable function whose rotation set contains at least countably many irrational rotations. In this paper we construct a function whose rotation set has uncountable intersection with each non-empty open subset of \(\mathbb R\). Cited in 2 Documents MSC: 28D05 Measure-preserving transformations Keywords:rotation set of a function Citations:Zbl 0869.28008 PDFBibTeX XMLCite \textit{R. E. Svetic}, Acta Math. Hung. 81, No. 4, 305--314 (1998; Zbl 0963.28013) Full Text: DOI