On the connectedness of self-affine attractors (Q1881521)

A self-affine attractor is an attractor of an affine iterated function system in Euclidean space, constructed by means of an expanding integral matrix and a set of displacement vectors. Under the assumption that such vectors are integral multiples of an arbitrary non-zero vector, the authors prove the connectedness of the attractor, in the three- and four-dimensional case. The authors then relate the above for studying the connectedness of the so-called dual tiling generated by Pisot units, establishing arc-wise connectedness of the tiles in the case of degree 3, and giving necessary and sufficient conditions for connectedness in degree 4. This paper is a preview of results which are to appear elsewhere.