Rank one subshifts are dynamical systems generated by a regular combinatorial process based on sequences of positive integers called the cut and spacer parameters. Despite the simple process that generates them, rank one subshifts comprise a generic set and are the source of many counterexamples. As a result, measure theoretic rank one subshifts, called rank one transformations, have been extensively studied and investigations into rank one subshifts been the basis of much recent work. We will answer several open problems about rank one subshifts. We completely classify the maximal equicontinuous factor for rank one subshifts, so that this factor can be computed from the parameters. We use these methods to classify when large classes of rank one subshifts have mixing properties. Also, we completely classify the situation when a rank one subshift can be a factor of another rank one subshift.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc1157623 |
| Date | 05 1900 |
| Creators | Ziegler, Caleb |
| Contributors | Gao, Su, Jackson, Stephen, Fishman, Lior |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | v, 86 pages, Text |
| Rights | Public, Ziegler, Caleb, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
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