Geometrical Models for Substitutions

被引：16

作者：

Arnoux, Pierre ^{[1
]}

Bernat, Julien ^{[2
,3
]}

Bressaud, Xavier ^{[4
]}

机构：

[1] CNRS, Inst Math Luminy, UMR 6206, F-13288 Marseille 09, France

[2] Univ Nancy 1, IUFM Lorraine, F-54506 Vandoeuvre Les Nancy, France

[3] Univ Nancy 1, CNRS, Inst Elie Cartan, UMR 7502, F-54506 Vandoeuvre Les Nancy, France

[4] Univ Toulouse 3, Inst Math Toulouse, F-31062 Toulouse 9, France

来源：

EXPERIMENTAL MATHEMATICS | 2011年 / 20卷 / 01期

关键词：

Interval exchange transformations; Rauzy fractals; substitutive dynamical systems; Peano curves; INTERVAL EXCHANGE;

D O I：

10.1080/10586458.2011.544590

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a substitution associated with the Arnoux-Yoccoz interval exchange transformation (IET) related to the tribonacci substitution. We construct the so-called stepped lines associated with the fixed points of the substitution in the abelianization (symbolic) space. We analyze various projections of the stepped line, recovering the Rauzy fractal, a Peano curve related to work in [Arnoux 88], another Peano curve related to the work of [Mc-Mullen 09] and [Lowenstein et al. 07], and also the interval exchange transformation itself.

引用

页码：97 / 127

页数：31

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