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The rotation class of a flow. (English) Zbl 1074.37008
Summary: Generalizing a construction of A. Weil [J. Indian Math. Soc. 19, 109–114 (1931; JFM 57.0503.03 and Zbl 0003.25501) and Rec. Math. Moscou, n. Ser. 1, 779–781 (1936; JFM 62.0665.03 and Zbl 0016.08601)], we introduce a topological invariant for flows on compact, connected, finite-dimensional, Abelian, topological groups. We calculate this invariant for some examples.
MSC:
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37B45 Continua theory in dynamics
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[1] Aranson, S.Kh.; Belitsky, G.R.; Zhuzhoma, E.V., Introduction to the qualitative theory of dynamical systems on surfaces, Transl. math. monographs, vol. 153, (1996), American Mathematical Society Providence, RI · Zbl 0853.58090
[2] Aranson, S.Kh.; Zhuzhoma, E.V., The topological classification of singular dynamical systems on the torus, Izv. vyssh. uchebn. zaved. mat., 5, 168, 104-107, (1976) · Zbl 0335.34026
[3] Clark, A., Linear flows on κ-solenoids, Topology appl., 94, 27-49, (1999) · Zbl 0929.37012
[4] Clark, A., Solenoidalization and denjoids, Houston J. math., 26, 661-692, (2000) · Zbl 1007.37008
[5] Fuchs, L., Infinite abelian groups, (1970), Academic Press New York · Zbl 0213.03501
[6] McCord, M.C., Inverse limit sequences with covering maps, Trans. amer. math. soc., 114, 197-209, (1965) · Zbl 0136.43603
[7] Scheffer, W., Maps between topological groups that are homotopic to homomorphisms, Proc. amer. math. soc., 33, 2, 562-567, (1972) · Zbl 0236.22008
[8] Weil, A., LES families de courbes sur le tore, Mat. sb., 1, 779-781, (1936) · Zbl 0016.08601
[9] Weil, A., On systems of curves on a ring-shaped surface, J. Indian math. soc., 19, 109-114, (1931) · JFM 57.0503.03
[10] de Vries, J., Elements of topological dynamics, (1993), Kluwer Academic Dordrecht · Zbl 0783.54035
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