Substitution dynamical systems on infinite alphabets

被引：22

作者：

Ferencz, Sebastien

机构：

[1] Inst Math Luminy, CNRS, UPR 9016, F-13288 Marseille 9, France

[2] Federat REch Unites Math Marseille, CNRS FR 2291, Marseille, France

来源：

ANNALES DE L INSTITUT FOURIER | 2006年 / 56卷 / 07期

关键词：

substitutions; dynamical systems;

D O I：

10.5802/aif.2242

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a few examples of substitutions on infinite alphabets, and the beginning of a general theory of the associated dynamical systems. In particular, the "drunken man" substitution can be associated to an ergodic infinite measure preserving system, of Krengel entropy zero, while substitutions of constant length with a positive recurrent infinite matrix correspond to ergodic finite measure preserving systems.

引用

页码：2315 / 2343

页数：29

共 12 条

[1] Complexity and special factors [J].

Cassaigne, J .

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 1997, 4 (01) :67-88

[2] A characterization of substitutive sequences using return words [J].

Durand, F .

DISCRETE MATHEMATICS, 1998, 179 (1-3) :89-101

[3] Complexity of sequences and dynamical systems [J].

Ferenczi, S .

DISCRETE MATHEMATICS, 1999, 206 (1-3) :145-154

[4]

FOGG NP, 2002, LECT NOTES MATH, V1794

[5]

FOGG NP, UNPUB UNIVERSAL COUN

[6]

Hopf E., 1937, Ergodentheorie

[7]

KITCHENS B, 1998, SYMBOLIC DYNAMICS 1

[8] ENTROPY OF CONSERVATIVE TRANSFORMATIONS [J].

KRENGEL, U .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1967, 7 (03) :161-&

[9]

LEGONIDEC M, IN PESS ANN I FOURIE

[10]

MAUDUIT C, IN PRESS ANN I FOURI

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