PURE DISCRETE SPECTRUM FOR A CLASS OF ONE-DIMENSIONAL SUBSTITUTION TILING SYSTEMS

被引：9

作者：

Barge, Marcy ^{[1
]}

机构：

[1] Montana State Univ, Dept Math Sci, Bozeman, MT 59717 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 03期

关键词：

Substitution; tiling space; discrete spectrum; maximal equicontinuous factor; PISOT SUBSTITUTIONS; COINCIDENCE; DYNAMICS;

D O I：

10.3934/dcds.2016.36.1159

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that if a primitive and non-periodic substitution is injective on initial letters, constant on final letters, and has Pisot inflation, then the R-action on the corresponding tiling space has pure discrete spectrum. As a consequence, all beta-substitutions for beta a Pisot simple Parry number have tiling dynamical systems with pure discrete spectrum, as do the Pisot systems arising, for example, from substitutions associated with the Jacobi-Perron and Brun continued fraction algorithms.

引用

页码：1159 / 1173

页数：15

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