We consider Livsic regularity for Lie group valued cocycles over: a class of piecewise expanding maps of the interval, namely Lasota-Yorke maps; uniformly hyperbolic toral maps with singularities and a class of nonuniformly expanding interval maps. As applications of the results we prove stable ergodicity theorems for compact Lie group extension of Lasota-Yorke maps and uniformly hyperbolic toral maps with singularities. Additionally we consider conditions for the ergodicity and weak-mixing of finite group extensions of hyperbolic basic sets given in terms of periodic data and cohomological equations. We also consider stable ergodicity results for a class of nonconnected compact Lie group extensions of hyperbolic basic sets.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:396638 |
| Date | January 2003 |
| Creators | Scott, Andrew D. |
| Publisher | University of Surrey |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://epubs.surrey.ac.uk/844054/ |
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