Disk-like self-affine tiles in \(\mathbb{R}^2\). (English) Zbl 1020.52018
The authors give simple necessary and sufficient conditions for self-affine \({\mathbb Z}^2\)-tiles in \({\mathbb R}^2\) to be homeomorphic to a disk. These conditions are formulated in terms of \({\mathcal F}\)-connectedness of the digit set of a tile, where \({\mathcal F}\) is a (sub-)set of neighbors of a tile.
Reviewer: Elena E.Berdysheva (Stuttgart)