The thesis consists of two main results. The first main result is a proof that C^1 rigidity holds for circle maps with a break point for almost all rotation numbers. The second main result is a proof that C^1 robust rigidity holds for circle maps in the fractional linear transformation (FLT) pair family. That is, for this family, C^1 rigidity holds for all irrational rotation numbers. The approach taken here of proving a more general theorem that C^1 rigidity holds for circle maps with a break point satisfying a `derivatives close condition', allows us to obtain both of our main results as corollaries of this more general theorem.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/34807 |
| Date | 17 December 2012 |
| Creators | Mazzeo, Elio |
| Contributors | Khanin, Konstantin |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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