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Some problems of attractors of dynamical systems. (With an appendix written by N. E. Klinshpont). (English) Zbl 0847.54039

Summary: We discuss the problem of homeomorphism of attractors of dynamical systems, the classification problem and the problem of the topological structure of differentiable manifolds which allow dynamical systems with strange attractors.

MSC:

54H20 Topological dynamics (MSC2010)
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
54B20 Hyperspaces in general topology
54F50 Topological spaces of dimension \(\leq 1\); curves, dendrites
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[1] Afraimovich, V. S.; Bykov, V. V.; Shil’nicov, L. P., On structurally unstable attracting limit set of the type of the Lorenz attractor, Trans. Moskow Math. Soc., 44, 153-216 (1982) · Zbl 0527.58024
[2] Klinshpont, N. E., The topological invariant of the Lorenz attractor, Russian Math. Surveys, 47, 2, 195-196 (1992) · Zbl 0799.58046
[3] Williams, R. F., The structure of Lorenz attractors, Publ. Math. Inst. Hautes Étud. Sci. Ser. C, 50, 73-100 (1979) · Zbl 0484.58021
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