TY - JOUR

T1 - Divergent coindex sequence for dynamical systems

AU - Shi, Ruxi

AU - Tsukamoto, Masaki

N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85126434170&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85126434170&partnerID=8YFLogxK

U2 - 10.1142/S1793525322500042

DO - 10.1142/S1793525322500042

M3 - Article

AN - SCOPUS:85126434170

SN - 1793-5253

JO - Journal of Topology and Analysis

JF - Journal of Topology and Analysis

ER -