Divergent coindex sequence for dynamical systems

Ruxi Shi, Masaki Tsukamoto

Research output: Contribution to journalArticlepeer-review

Abstract

When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between this index theory and topological dynamics. Given a fixed-point free dynamical system, the set of p-periodic points admits a natural free action of /p for each prime number p. We are interested in the growth of its index and coindex as p →∞. Our main result shows that there exists a fixed-point free dynamical system having the divergent coindex sequence. This solves a problem posed by M. Tsukamoto, M. Tsutaya and M. Yoshinaga, G-index, topological dynamics and marker property, preprint (2020), arXiv: 2012.15372.

Original languageEnglish
JournalJournal of Topology and Analysis
DOIs
Publication statusAccepted/In press - 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

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