The Garden of Eden theorem for linear cellular automata

被引：25

作者：

Ceccherini-Silberstein, T

Coornaert, M

机构：

[1] Univ Sannio, Dipartimento Ingn, I-82100 Benevento, Italy

[2] Univ Strasbourg 1, Inst Rech Math Avancee, F-67084 Strasbourg, France

[3] CNRS, F-67084 Strasbourg, France

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2006年 / 26卷

关键词：

D O I：

10.1017/S0143385705000520

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let V be a finite-dimensional vector space over a field K and let G be a countable amenable group. Let tau: V-G -> V-G be a linear cellular automaton. We prove that tau is surjective if and only if it is pre-injective.

引用

页码：53 / 68

页数：16

共 24 条

[1]

ADYAN SI, 1983, MATH USSR IZV, V21, P425, DOI 10.1070/IM1983v021n03ABEH001799

[2]

[Anonymous], P STEKLOV I MATH

[3]

Beck A, 1973, LECT NOTES MATH, V318, P120

[4] Amenable groups and cellular automata [J].

Ceccherini-Silberstein, TG ;

Machì, A ;

Scarabotti, F .

ANNALES DE L INSTITUT FOURIER, 1999, 49 (02) :673-+

[5] BRAID-GROUPS AND LEFT DISTRIBUTIVE OPERATIONS [J].

DEHORNOY, P .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 345 (01) :115-150

[6] The spectral measure of certain elements of the complex group ring of a wreath prod [J].

Dicks, W ;

Schick, T .

GEOMETRIAE DEDICATA, 2002, 93 (01) :121-137

[7]

Folner E., 1955, MATH SCAND, V3, P245

[8]

Greenleaf F., 1969, NOSTRAND MATH STUD S, V16

[9] The lamplighter group as a group generated by a 2-state automaton, and its spectrum [J].

Grigorchuk, RI ;

Zuk, A .

GEOMETRIAE DEDICATA, 2001, 87 (1-3) :209-244

[10] On a question of Atiyah [J].

Grigorchuk, RI ;

Linnell, P ;

Schick, T ;

Zuk, A .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 331 (09) :663-668

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