Dual systems of algebraic iterated function systems
Dual systems of algebraic iterated function systems
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DOI：
10.1016/j.aim.2013.11.010
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发表时间：
2014-03
影响因子：
1.7
通讯作者：
H. Rao;Z. Wen;Ya-min Yang
中科院分区：
文献类型：
--
作者：
H. Rao;Z. Wen;Ya-min Yang
研究了R上一类带代数参数的图定向迭代函数系统，我们称之为代数GIFS。我们构造了一个代数GIFS的对偶IFS，并研究了这两个系统之间的关系。我们确定一个对偶系统何时满足开集条件，这是基本的。对于可行的Pisot系统，我们构造了左Rauzy-Thurston镶嵌和右Rauzy-Thurston镶嵌，并研究了它们的重数和分解。我们还研究了它们与编码空间、域交换变换和Pisot谱猜想的关系。对偶IFS为Rauzy分形、β-tilings及相关研究提供了一个统一而简单的框架，使我们能够更好地理解。
We study a class of graph-directed iterated function systems on R with algebraic parameters, which we call algebraic GIFS. We construct a dual IFS of an algebraic GIFS, and study the relations between the two systems. We determine when a dual system satisfies the open set condition, which is fundamental. For feasible Pisot systems, we construct the left and right Rauzy–Thurston tilings, and study their multiplicities and decompositions. We also investigate their relation with codings space, domain-exchange transformation, and the Pisot spectrum conjecture. The dual IFS provides a unified and simple framework for Rauzy fractals, β-tilings and related studies, and allows us gain better understanding.