Undecidable properties of self-affine sets and multitape automata
We study the decidability of the topological properties of some objects coming from fractal geometry. We prove that having empty interior is undecidable for the sets defined by two-dimensional graph-directed iterated function systems. These results are obtained by studying a particular class of self-affine sets associated with multi-tape automata.
Timo Jolivet is a postdoctoral researcher at the Institut de Mathématiques de Toulouse at Université Paul Sabatier, funded by LabEx CIMI. He defended his PhD thesis in November 2013, under the co-supervision of Valérie Berthé (Université Paris Diderot, France) and Jarkko Kari (University of Turku, Finland). During the spring of 2014, he visited Montanuniversität Leoben and TU Graz (Austria).