Topological conjugacy for multifunctions with finitely many set-valued points and an application to iterative roots

Abstract

Topological conjugacy plays an important role in simplifying the systems and equations in the research of dynamical systems and functional equations. In this paper, we deal with increasing upper semi-continuous multifunctions with finitely many set-valued points. Some sufficient and necessary conditions are given for the topological conjugate relation between those multifunctions, and the methods of construction for all conjugacies are also presented. Moreover, as an application, our results are applied to study the problem of iterative roots for the multifunctions with a unique set-valued point.