Kato's chaos of multiple mappings and its continuous self-maps

Abstract

In 2016, Hou and Wang introduced the concept of multiple mappings based on iterated function system, which is an important branch of fractal theory. In this paper, we introduce the definitions of sensitivity, accessibility, and Kato's chaos of multiple mappings from a set-valued perspective. We show that multiple mappings and its continuous self-maps do not imply each other in terms of sensitivity and accessibility. While a sufficient condition for multiple mappings to be sensitive, accessible and Kato's chaotic is provided, respectively. And the sensitivity, accessibility, and Kato's chaos of multiple mappings are preserved under topological conjugation.