Atomic surfaces, tilings and coincidence I. Irreducible case
Atomic surfaces, tilings and coincidence I. Irreducible case
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DOI：
10.1007/bf02771781
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发表时间：
2006-01-01
影响因子：
1
通讯作者：
Rao, H.
中科院分区：
文献类型：
--
作者：
Ito, Shunji;Rao, H.
不可约Pisot代换定义了一个图定向迭代函数系统。这种迭代函数系统的不变集称为原子曲面。在本文中，一个新的原子表面，其中包含Thurston的β-平铺作为一个子类，平铺构造。相关的平铺和动力学性质进行了研究。在Dekking [Dek]定义的符合条件的基础上，引入了超符合条件。结果表明，超符合条件支配原子表面的平铺和动力学性质。我们猜想每一个Pisot代换都满足超符合条件。
An irreducible Pisot substitution defines a graph-directed iterated function system. The invariant sets of this iterated function system are called the atomic surfaces. In this paper, a new tiling of atomic surfaces, which contains Thurston's beta-tiling as a subclass, is constructed. Related tiling and dynamical properties are studied. Based on the coincidence condition defined by Dekking [Dek], we introduce the super-coincidence condition. It is shown that the super-coincidence condition governs the tiling and dynamical properties of atomic surfaces. We conjecture that every Pisot substitution satisfies the super-coincidence condition.