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\(\mathcal{F}\)-hypercyclic and disjoint \(\mathcal{F}\)-hypercyclic properties of binary relations over topological spaces. (English) Zbl 1495.47024

Summary: We examine various types of \(\mathcal{F}\)-hypercyclic (\(\mathcal{F}\)-topologically transitive) and disjoint \(\mathcal{F}\)-hypercyclic (disjoint \(\mathcal{F}\)-topologically transitive) properties of binary relations over topological spaces. We pay special attention to finite structures like simple graphs, digraphs and tournaments, providing a great number of illustrative examples.

MSC:

47A16 Cyclic vectors, hypercyclic and chaotic operators
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47D06 One-parameter semigroups and linear evolution equations
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