Algorithm for determining pure pointedness of self-affine tilings
نویسندگان
چکیده
منابع مشابه
Algorithm for Determining Pure Pointedness of Self-affine Tilings
Overlap coincidence in a self-affine tiling in R is equivalent to pure point dynamical spectrum of the tiling dynamical system. We interpret the overlap coincidence in the setting of substitution Delone set in R and find an efficient algorithm to check the pure point dynamical spectrum. This algorithm is easy to implement into a computer program. We give the program and apply it to several exam...
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By the algorithm implemented in Akiyama-Lee [3] and some of its predecessors, we have examined the pure discreteness of the spectrum for all irreducible Pisot substitutions of trace less than or equal to 2, and some cases of planar tilings generated by boundary substitutions due to Kenyon[17].
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We study self-affine tilings of R n with special emphasis on the two-digit case. We prove that in this case the tile is connected and, if n 3, is a lattice-tile.
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It is proved that every pseudo-self-affine tiling in R is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Voronöı tessellations is a corollary. Previously, these results were obtained in the planar case, jointly with Priebe Frank. The new approach is based on the theory of graph-directed iterated function systems and su...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2011
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.07.019