14 citations · 24 across the 6 of their papers we have counts for
9 papers
Topological substitutions and Rauzy fractals
Nicolas Bédaride, Arnaud Hilion, Timo Jolivet
We consider two families of planar self-similar tilings of different nature: the tilings consisting of translated copies of the fractal sets defined by an iterated function system,…
A numerical scale for non locally connected planar continua
Timo Jolivet, Benoît Loridant, Jun Luo
We introduce a numerical scale to quantify to which extent a planar continuum is not locally connected. For a locally connected continuum, the numerical scale is zero; for a contin…
Undecidable properties of self-affine sets and multi-tape automata
Timo Jolivet, Jarkko Kari
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…
A combinatorial approach to products of Pisot substitutions
Valérie Berthé, Jérémie Bourdon, Timo Jolivet +1
We define a generic algorithmic framework to prove pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substituti…
Rauzy fractals with countable fundamental group
Timo Jolivet, Benoît Loridant, Jun Luo
We prove that every free group of finite rank can be realized as the fundamental group of a planar Rauzy fractal associated with a 4-letter unimodular cubic Pisot substitution. Thi…
Critical connectedness of thin arithmetical discrete planes
Valérie Berthé, Damien Jamet, Timo Jolivet +1
An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its -connectedness. This…