Robust Density of Periodic Sinks and Sources for Iterated Function Systems

Abstract

Given any compact m-dimensional manifold M , we describe C 1open sets of iterated function systems admitting infinite number of attracting and repelling periodic orbits. We show that attracting periodic orbits are dense in the ambient manifold M . Also, the same property holds for repelling periodic orbits.Moreover, the step skew product maps corresponding to these iterated function systems are topologically transitive.