On cut sets of attractors of iterated function systems (Q2817011)

Let \(T\) be a connected attractor of an IFS consisting of injective contractions on \(\mathbb{R}^{d}\). A subset \(X\) of \(T\) is a cut set if \( T\setminus X\) is disconnected. Further, a cut set \(X\) is irreducible if \( T\setminus X_{0}\) is connected for any proper subset \(X_{0}\) of \(X\) which is closed in \(T\). In the paper under review, the authors provide sufficient conditions for an irreducible cut set of \(T\) to be perfect (i.e., free of isolated points) or to be a singleton. For a special sort of \(T\) (integral self-affine tiles with standard digit set), the authors show that those sufficient conditions can be checked algorithmically. Finally, they exhibit a method of detecting cut points of those special attractors.