The Global Structure of Iterated Function Systems

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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].

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Snyder, Jason Edward May 2009.

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  • Snyder, Jason Edward

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Description

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].

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  • May 2009

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  • Oct. 10, 2009, 4:41 p.m.

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  • Jan. 14, 2014, 4:08 p.m.

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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/: accessed June 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .