Minimal sets in compact connected subspaces
Consider a topological discrete dynamical system \((X,f)\), where \(X\) is a topological space and \(f: X\to X\) a continuous self-map. Let \(Y\subset X\) be a compact, connected and closed subset of \(X\). The objective of the present paper is to show that if the boundary \(\partial_XY\) contains exactly one point \(v\) and \(f(v)\in Y\), then \(Y\) contains a minimal set of \(f\).
scientific article; zbMATH DE number 5956071
scientific article