G-index, topological dynamics and the marker property

被引：2
|
作者：
Tsukamoto, Masaki [1 ]
Tsutaya, Mitsunobu [1 ]
Yoshinaga, Masahiko [2 ]
机构：
[1] Kyushu Univ, Dept Math, Nishi Ku, Moto Oka 744, Fukuoka 8190395, Japan
[2] Hokkaido Univ, Dept Math, Kita Ku, North 10,West 8, Sapporo, Hokkaido 0600810, Japan
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2022年 / 251卷 / 02期
关键词：
DOUBLE VARIATIONAL PRINCIPLE; MEAN DIMENSION;
D O I：
10.1007/s11856-022-2433-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given an action of a finite group G on a topological space, we can define its index. The G-index roughly measures a size of the given G-space. We explore connections between the G-index theory and topological dynamics. For a fixed-point free dynamical system, we study the Z(p)-index of the set of p-periodic points. We find that its growth is at most linear in p. As an application, we construct a free dynamical system which does not have the marker property. This solves a problem which has been open for several years.
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页码：737 / 764
页数：28
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