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:LACETR/oai:collectionscanada.gc.ca:OTU.1807/34807 |
Date | 17 December 2012 |
Creators | Mazzeo, Elio |
Contributors | Khanin, Konstantin |
Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
Language | en_ca |
Detected Language | English |
Type | Thesis |
Page generated in 0.0017 seconds