The Global Structure of Iterated Function Systems

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].

Creator(s): Snyder, Jason Edward
Creation Date: May 2009
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
Usage:
Total Uses: 168
Past 30 days: 17
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Creator (Author):
Publisher Info:
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
Date(s):
  • Creation: May 2009
  • Digitized: October 2, 2009
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].

Degree:
Level: Doctoral
Discipline: Mathematics
Language(s):
Subject(s):
Keyword(s): dimension | Iterated function systems | attractor | non-attractor
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • OCLC: 460925936 |
  • UNTCAT: b3799567 |
  • ARK: ark:/67531/metadc9917
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Public
License: Copyright
Holder: Snyder, Jason Edward
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.