Sensitivity and chaos of iterated function systems
The present work is concerned with sensitivity and chaos for iterated function systems (IFSs) First of all, we introduce the concept of S transitivity for IFSs which is relevant with sensitive dependence on initial condition. That yields to a different example of non minimal sensitive system which is not an M system. Also, several sufficient conditions for sensitivity of IFSs are presented. Furthermore, we will study the most two popular definitions of chaos, given by Li Yorke and Devaney, which are generalized for iterated function systems. At last, we give several conditions that guarantee the occurrence of densely Li Yorke chaos and Devaney chaos for IFSs.