Non-autonomous iterated function systems and fractals (Research on the Theory of Random Dynamical Systems and Fractal Geometry)

Abstract

We consider non-autonomous iterated function systems (NAIFSs). NAIFSs are generalization of the iterated function systems and are an important method to construct generalized fractals (limit sets). However, many researchers only deal with NAIFSs defined on bounded sets (in some sense) or compact sets. The aim of this paper is to present a method to construct the limit sets (and the limit measures) generated by NAIFSs (with weights) defined on complete (separable) metric spaces, which has not been discussed before. If an NAIFS (with weights) satisfies a "good" condition, we can construct the limit sets (and the limit measures) generated by the NAIFS (with weights). We also discuss some basic properties. Besides, this paper presents some examples of NAIFSs.