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Rotation sets for homeomorphisms and homology. (English) Zbl 0758.58018
The article gives a new definition of rotation set for homeomorphism of arbitrary compact manifold \(M\). This is a generalization of a rotation number of a homeomorphism of unit circle. A rotation set of the homeomorphism isotopic to identity is some subset of the real homology \(H_ 1(M,R)\). The construction of the rotation set is found in the paper “Asymptotic cycles” [Ann. Math., II. Ser. 66, 270-284 (1957; Zbl 0207.226)] by S. Schwartzman. The proposed definition differs from the known ones. The main application is to give a generalization of a theorem of Llibre and MacKay to the surfaces of higher genus. There are many examples.

MSC:
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37C10 Dynamics induced by flows and semiflows
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