TOPOLOGICAL TRANSITIVITY AND CHAOS OF GROUP ACTIONS ON DENDRITES

被引：6

作者：

Wang, Suhua ^{[1
]}

Shi, Enhui ^{[1
]}

Zhou, Lizhen ^{[1
]}

Su, Xunli ^{[2
]}

机构：

[1] Suzhou Univ, Dept Math, Suzhou 215006, Peoples R China

[2] Suzhou Univ Sci & Technol, Dept Math, Suzhou 215011, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2009年 / 19卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Topological transitivity; weak mixing; chaos; group action; dendrite; GEOMETRIC ENTROPY; PEANO-CONTINUA; MAPS; SETS;

D O I：

10.1142/S0218127409025274

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that each weakly mixing group action on a dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated. As a corollary, we prove that no nilpotent group action on a dendrite is weakly mixing. At last, we show that each dendrite admits no chaotic group actions.

引用

页码：4165 / 4174

页数：10

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