Syndetically transitive and syndetically sensitive Iterated Function Systems

Abstract

Abstract In this paper, we discuss several stronger forms of sensitivities for iterated function systems (IFSs), such as strong sensitivity and syndetical sensitivity, and obtain some sufficient conditions for an IFS to have such sensitivities. We pay special attention to IFSs acting on the circle S1. We prove that each sensitive IFS acting on the circle S1 generating by a finite family of circle homeomorphisms is strongly sensitive. However, to obtain syndetical sensitivity, we impose some extra conditions on the IFS. Finally, we study sensitivity properties for syndetical transitive IFSs. We show that each syndetically transitive IFS is topologically ergodic.