Tilings from non-Pisot unimodular matrices

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概要

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• Using the unimodular Pisot substitution of the free monoid on $d$ letters, the existence of graph-directed self-similarsets$\left\{ X_{i} \right\}_{i=1,2,\ldots,d}$satisfying the set equation (\ref{eq:pisot})with the positive measure on the $A$-invariant contracting plane $P$ is well-known,where $A$ is the incidence matrix of the substitution.Moreover, under some conditions, the set$\left\{ X_{i} \right\}_{i=1,2,\ldots,d}$is the prototile of the quasi-periodictiling of $P$ (see Figure \ref{fig:Rauzy}). In this paper, even in the case of non-Pisot matrix $A$, the generating method of graph-directed self-similar sets and quasi-periodic tilings is proposed under the "blocking condition".

• 広島大学の論文

著者

• Furukado Maki

  Faculty Of Business Administration Yokohama National University

関連論文

• Tilings from non-Pisot unimodular matrices

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