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Rotation sets and ergodic measures for torus homeomorphisms. (English) Zbl 0739.58033
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)

MSC:
37A99 Ergodic theory
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