Misiurewicz, Michał; Ziemian, Krystyna Rotation sets and ergodic measures for torus homeomorphisms. (English) Zbl 0739.58033 Fundam. Math. 137, No. 1, 45-52 (1991). Authors’ abstract: “We prove that for every homeomorphism \(f\) of the two-dimensional torus onto itself isotopic to the identity and a vector \(v\) from the interior of the rotation set of \(f\) there exists a closed non-empty invariant set whose each point has rotation vector \(v\). It follows that there exists an ergodic invariant probability measure on the torus such that the expected value of the displacement by \(f\) is \(v\). We also show examples that this is not necessarily true if \(v\) is from the boundary of the rotation set of \(f\), even if the interior of this set is non-empty.”. Reviewer: L.Stoyanov (Sofia) Cited in 34 Documents MSC: 37A99 Ergodic theory Keywords:two-dimensional torus; rotation vector; ergodic invariant probability measure PDFBibTeX XMLCite \textit{M. Misiurewicz} and \textit{K. Ziemian}, Fundam. Math. 137, No. 1, 45--52 (1991; Zbl 0739.58033) Full Text: DOI EuDML