Coboundary on colored tiling space as Rauzy fractal
Coboundary on colored tiling space as Rauzy fractal
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彩色平铺空间上的共界为 Rauzy 分形
DOI：
10.1016/s0019-3577(99)80032-9
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
T. Kamae
中科院分区：
文献类型：
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作者：
Nertila Gjini;T. Kamae
本文考虑了[1]中作者之一所引入的加权代换所对应的色镶嵌空间Ω，它是分段线性f的f-展开式的一种自然推广。给出了整点空间Ω0上α-G-齐次的适应上边界的一个特征，其中α是一个具有负真实的部分的复数.对应于三次Pisot型加权代换的这种上边界的像是一个分形集，称为Rauzy分形。我们还考虑了Fibonacci镶嵌及其上的α-G-齐次的自适应余边界，这个余边界与分数部分一起给出了Fibonacci展开式的几何表示，这或多或少是已知的。
We consider the space Ω of colored tilings corresponding to a weighted substitution introduced by one of the authors in [1], which is a kind of natural extension of the f-expansion for a piecewise linar f. We give a characterization of adapted coboundaries, which are α-G-homogeneous on the space of integer points Ω0, where α is a complex number with a negative real part. The image of such a coboundary corresponding to a weighted substitution of cubic Pisot type, is a fractal set called Rauzy fractal. We also consider the Fibonacci tiling and the α-G-homogeneous, adapted coboundary on it. This coboundary together with the fractional part give a geometrical representation of the Fibonacci expansions that is more or less known.