Abstract
This paper presents results on rotation numbers for orientation-preserving torus homeomorphisms homotopic to a Dehn twist. Rotation numbers and the rotation set for such homeomorphisms have been defined and initially investigated by the first author in a previous paper. Here we prove that each rotation number in the interior of the rotation set is realized by some compact invariant set, and that there is an ergodic measure on that set with mean rotation number . It is also proved that the function which assigns its rotation set to such a homeomorphism is continuous. Finally, a counterexample is presented that shows that rational extremal points of the shear rotation set do not necessarily correspond to any periodic orbits.
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