On a family of IFSs whose attractors are not connected (Q624569)

On a given Banach space \(X\), the authors consider a family of Iterated Function Systems (IFSs) composed by two affine contractions and indexed by the free term of the second contraction, such that the linear operator from the definition of the first contraction is finite dimensional. Using a well known result concerning the connectivity of the attractor of an IFS, they prove that the set of the free terms of the second contraction for which the attractor is disconnected is open and dense in \(X\). In this way, a connection between the theory of IFSs and the theory of finite dimensional operators is established.