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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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