Pure discrete spectrum dynamical system and periodic tiling associated with a substitution

被引：13

作者：

Siegel, A ^{[1
]}

机构：

[1] CNRS, IRISA, UMR 6074, F-35042 Rennes, France

来源：

ANNALES DE L INSTITUT FOURIER | 2004年 / 54卷 / 02期

关键词：

substitution; dynamical system; pure discrete spectrum; Rauzy fractals; tiling;

D O I：

10.5802/aif.2021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a computable sufficient condition for the symbolic dynamical system associated with a substitution of Pisot type to have a pure discrete spectrum. In the unimodular case, this condition is necessary when the substitution has no nontrivial coboundary; it is satisfied if and only if the Rauzy fractal associated with the substitution generates a self-similar periodic tiling. Conditions for connectivity of Rauzy fractals are deduced.

引用

页码：341 / +

页数：42

共 27 条

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