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].
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc9917 |
| Date | 05 1900 |
| Creators | Snyder, Jason Edward |
| Contributors | Urbański, Mariusz, Mauldin, R. Daniel, Cherry, William, 1966-, Skorulski, Bartlomiej |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Copyright, Snyder, Jason Edward, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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