Certain discrete dynamical systems, number systems and related integral self-affine sets

We consider certain discrete dynamical systems, conventional number systems and redundant number systems for Z2, which are associated with certain 2×2 integral expansive matrices and collinear digit sets for them. Using integral self-affine sets in Rn we also give a geometric characterization to attractors of certain discrete dynamical systems and associated redundant number systems for Zn.