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Currently displaying 1 – 2 of 2

Order by Relevance | Title | Year of publication

Complex Pisot Numeration Systems

Maki Furukado; Shunji Ito — 2009

Actes des rencontres du CIRM

Tilings associated with non-Pisot matrices

Maki Furukado; Shunji Ito; E. Arthur Robinson — 2006

Annales de l’institut Fourier

Suppose $A \in G l_{d} (ℤ)$ has a 2-dimensional expanding subspace $E^{u}$ , satisfies a regularity condition, called “good star”, and has $A^{*} \geq 0$ , where $A^{*}$ is an of $A$ . A morphism $θ$ of the free group on ${1, 2, \dots, d}$ is called a of $A$ if it has structure matrix $A$ . We show that there is a $Θ$ whose “boundary substitution” $θ = \partial Θ$ is a non-abelianization of $A$ . Such a tiling substitution $Θ$ leads to a self-affine tiling of $E^{u} \sim ℝ^{2}$ with $A_{u} {: = A |}_{E_{u}} \in G L_{2} (ℝ)$ as its expansion. In the last section we find conditions on $A$ so that $A^{*}$ has no negative entries.

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