Constant-length substitutions and countable scrambled sets

被引：19

作者：

Blanchard, F

Durand, F

Maass, A

机构：

[1] CNRS, FRUMAM, UPR 9016, Inst Math Luminy, F-13288 Marseille 09, France

[2] Univ Picardie, CNRS, UMR 6140, Lab Amienois Math Fondamentales & Appl, F-80000 Amiens, France

[3] Univ Chile, Dept Ingn Matemat, Santiago, Chile

[4] UCHILE, CNRS, UMR 2071, Ctr Modelamiento Matemat, Santiago, Chile

来源：

NONLINEARITY | 2004年 / 17卷 / 03期

关键词：

D O I：

10.1088/0951-7715/17/3/005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we provide examples of topological dynamical systems having either finite or countable scrambled sets. In particular we study conditions for the existence of Li-Yorke, asymptotic and distal pairs in constant-length substitution dynamical systems. Starting from a circle rotation, we also construct a dynamical system having Li-Yorke pairs, none of which is recurrent.

引用

页码：817 / 833

页数：17

共 12 条

[1]

AKIN E, CONCEPTS ELLIS ACTIO

[2]

Auslander J., 1988, MATH STUDIES, V153

[3] Asymptotic orbits of primitive substitutions [J].

Barge, M ;

Diamond, B ;

Holton, C .

THEORETICAL COMPUTER SCIENCE, 2003, 301 (1-3) :439-450

[4]

Blanchard F, 2002, J REINE ANGEW MATH, V547, P51

[5] ON THE PERIODICITY OF MORPHISMS ON FREE MONOIDS [J].

HARJU, T ;

LINNA, M .

RAIRO-INFORMATIQUE THEORIQUE ET APPLICATIONS-THEORETICAL INFORMATICS AND APPLICATIONS, 1986, 20 (01) :47-54

[6] Directed graphs and substitutions [J].

Holton, C ;

Zamboni, LQ .

THEORY OF COMPUTING SYSTEMS, 2001, 34 (06) :545-564

[7] PERIOD 3 IMPLIES CHAOS [J].

LI, TY ;

YORKE, JA .

AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (10) :985-992

[8]

MIGNOSI F, 1993, LECT NOTES COMPUTER, V700, P507

[9] Recognizability of substitutions and complexity of automatic sequences [J].

Mosse, B .

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1996, 124 (02) :329-346

[10]

QUEFFELEC M, 1987, LECT NOTES MATH, V1294

← 1 2 →