G-index, topological dynamics and the marker property

Masaki Tsukamoto, Mitsunobu Tsutaya, Masahiko Yoshinaga

Research output: Contribution to journalArticlepeer-review

Abstract

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 ℤp-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.

Original languageEnglish
Pages (from-to)737-764
Number of pages28
JournalIsrael Journal of Mathematics
Volume251
Issue number2
DOIs
Publication statusPublished - Dec 2022

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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