Topological mapping properties defined by digraphs (Q1576819)

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.