Expansive algebraic actions of countable abelian groups

被引：9

作者：

Miles, R ^{[1
]}

机构：

[1] Univ E Anglia, Norwich NR4 7TJ, Norfolk, England

来源：

MONATSHEFTE FUR MATHEMATIK | 2006年 / 147卷 / 02期

关键词：

expansiveness; algebraic action; integral domain; valuation;

D O I：

10.1007/s00605-005-0338-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper gives an algebraic characterization of expansive actions of countable abelian groups on compact abelian groups. This naturally extends the classification of expansive algebraic Z(d)-actions given by Schmidt using complex varieties. Also included is an application to a natural class of examples arising from unit subgroups of integral domains.

引用

页码：155 / 164

页数：10

共 50 条

[1] Expansive Algebraic Actions of Countable Abelian Groups
Richard Miles
Monatshefte für Mathematik, 2006, 147 : 155 - 164
[2] The entropy of algebraic actions of countable torsion-free abelian groups
Miles, Richard
FUNDAMENTA MATHEMATICAE, 2008, 201 (03) : 261 - 282
[3] Entropy of Gaussian actions for countable Abelian groups
Lemanczyk, M
FUNDAMENTA MATHEMATICAE, 1998, 157 (2-3) : 277 - 286
[4] Homoclinic groups, IE groups, and expansive algebraic actions
Chung, Nhan-Phu
Li, Hanfeng
INVENTIONES MATHEMATICAE, 2015, 199 (03) : 805 - 858
[5] Homoclinic groups, IE groups, and expansive algebraic actions
Nhan-Phu Chung
Hanfeng Li
Inventiones mathematicae, 2015, 199 : 805 - 858
[6] Entropy for expansive algebraic actions of residually finite groups
Bowen, Lewis
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2011, 31 : 703 - 718
[7] Pseudo-orbit tracing and algebraic actions of countable amenable groups
Meyerovitch, Tom
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2019, 39 : 2570 - 2591
[8] Expansive algebraic actions of discrete residually finite amenable groups and their entropy
Deninger, Christopher
Schmidt, Klaus
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 : 769 - 786
[9] THE COHOMOLOGY OF EXPANSIVE Z(D)-ACTIONS BY AUTOMORPHISMS OF COMPACT, ABELIAN-GROUPS
KATOK, AB
SCHMIDT, K
PACIFIC JOURNAL OF MATHEMATICS, 1995, 170 (01) : 105 - 142
[10] PERIODIC POINTS FOR EXPANSIVE ACTIONS OF Z(D) ON COMPACT ABELIAN-GROUPS
WARD, TB
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1992, 24 : 317 - 324

← 1 2 3 4 5 →