Attractors for iterated function systems

Abstract

Let X be a compact metric space with \mathcal S = \{S_{1}, \ldots, S_{N}\} a finite set of contraction maps from X to itself. Call a subset F of X an attractor for the iterated function scheme (IFS) \mathcal S if F = \bigcup_{i=1}^{N}S_{i}(F) . Working primarily on the unit interval I= [0,1] , we show that