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On the connectedness of the attainability set for lattice dynamical systems. (English) Zbl 1243.34012
Summary: We prove the Kneser property (i.e. the connectedness and compactness of the attainability set at any time) for lattice dynamical systems in which we do not know whether the property of uniqueness of the Cauchy problem holds or not. Using this property, we can check that the global attractor of the multivalued semiflow generated by such system is connected.

MSC:
34A33 Ordinary lattice differential equations
34D45 Attractors of solutions to ordinary differential equations
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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