5 citations · 11 across the 10 of their papers we have counts for
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A Core Decomposition of Compact Sets in the Plane
Benoit Loridant, Jun Luo, Yi Yang
A Peano continuum means a locally connected continuum. A compact metric space is called a \emph{Peano compactum} if all its components are Peano continua and if for any constant $C…
Geometrical models for a class of reducible Pisot substitutions
Benoit Loridant, Milton Minervino
We set up a geometrical theory for the study of the dynamics of reducible Pisot substitutions. It is based on certain Rauzy fractals generated by duals of higher dimensional extens…
Topology of a class of -crystallographic replication tiles
Benoît Loridant, Shu-qin Zhang
We study the topological properties of a class of planar crystallographic replication tiles. Let be an expanding matrix with characteristic polynomial $…
Topological properties of a class of cubic Rauzy fractals
Benoît Loridant
We consider the substitution defined by $$\begin{array}{rlcl} σ_{a,b}: & 1 & \mapsto & \underbrace{1\ldots 1}_{a}2 \\ & 2 & \mapsto & \underbrace{1\ldots 1}_{b}3 \\ & 3 &…
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…