Banks, John Topological mapping properties defined by digraphs. (English) Zbl 0957.54020 Discrete Contin. Dyn. Syst. 5, No. 1, 83-92 (1999). Let \(f:X\to X\) be a continuous map on the topological space \(X\) given by the family \({\mathcal S}\) of open sets. A graph \(G\) with directed edges \((u,v)\) \((u,v\in G)\) defines a mapping property if for any \(\varphi:G\to S\smallsetminus \emptyset\) there is \(k\geq 1\) such that \(f^k (\varphi(u))\cap \varphi(v)\neq \emptyset\) for every edge \((u,v)\) in \(G\). Several graphs are listed in the paper under review (including the non-wandering, transitivity and mixing properties) and their classification is given. Reviewer: Manfred Denker (Göttingen) Cited in 16 Documents MSC: 54H20 Topological dynamics (MSC2010) 37B20 Notions of recurrence and recurrent behavior in topological dynamical systems 28D99 Measure-theoretic ergodic theory Keywords:topological weak mixing; mapping property; non-wandering; transitivity PDFBibTeX XMLCite \textit{J. Banks}, Discrete Contin. Dyn. Syst. 5, No. 1, 83--92 (1999; Zbl 0957.54020) Full Text: DOI