The Global Structure of Iterated Function Systems Page: I
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Snyder, Jason Edward. The Global Structure of Iterated Function Systems. Doctor of
Philosophy (Mathematics), May 2009, 50 pp., 5 figures, references, 12 titles.
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 F6 set and the space of all non-attractors is a dense G6 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].
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Snyder, Jason Edward. The Global Structure of Iterated Function Systems, dissertation, May 2009; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc9917/m1/2/: accessed January 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .