The Global Structure of Iterated Function Systems

• Main Author: Snyder, Jason Edward
• Other Authors: Urbański, Mariusz
• Format: Others
• Language: English
• Published: University of North Texas 2009
• Subjects: dimension; Iterated function systems; attractor; non-attractor; Iterative methods (Mathematics); Set theory.; Fractals.
• Online Access: https://digital.library.unt.edu/ark:/67531/metadc9917/

I study sets of attractors and non-attractors of finite iterated function systems. I provide examples of compact sets which are attractors of iterated function systems as well as compact sets which are not attractors of any iterated function system. I show that the set of all attractors is a dense Fs set and the space of all non-attractors is a dense Gd set it the space of all non-empty compact subsets of a space X. I also investigate the small trans-finite inductive dimension of the space of all attractors of iterated function systems generated by similarity maps on [0,1].