A note on expansive $\mathbb{Z}^k$-action and generators

Ekta Shah

doi:10.4134/CKMS.c180365

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2019; 34(4): 1329-1334

Online first article August 27, 2019 Printed October 31, 2019

https://doi.org/10.4134/CKMS.c180365

A note on expansive $\mathbb{Z}^k$-action and generators

Ekta Shah

The Maharaja Sayajirao University of Baroda

Abstract

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Abstract

We define the concept of a generator for a $\mathbb{Z}^k$-action $T$ and show that $T$ is expansive if and only it has a generator. Further, we prove several properties of a $\mathbb{Z}^k$-action including that the least upper bound of the set of expansive constants is not an expansive constant.

Keywords: expansive homeomorphisms, generators, $\mathbb{Z}^k$-actions

MSC numbers: Primary 37B99; Secondary 54H20