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Rotation sets for maps of tori. (English) Zbl 0663.58022
The notion of a rotation set of a continuous map of an n-dimensional torus into itself, homotopic to the identity, generalizes the notions of the rotation number (for homeomorphisms of a circle) and the rotation interval (for continuous maps of a circle). This notion is studied, with the discussion of several possible definitions and their relations to each other. The rotation set is always compact and connected. Stronger results can be obtained for homeomorphisms of a 2-dimensional torus. Then in particular the rotation set is convex and depends on the map in an upper semi-continuous way. In a general case some counterexamples are given.
Reviewer: M.Misiurewicz

MSC:
37A99 Ergodic theory
28D99 Measure-theoretic ergodic theory
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