Livsic theorems and the stable ergodicity of compact group extensions for systems with some hyperbolicity.

Scott, Andrew D. (2003) Livsic theorems and the stable ergodicity of compact group extensions for systems with some hyperbolicity. Doctoral thesis, University of Surrey (United Kingdom)..

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Abstract

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.

Item Type:	Thesis (Doctoral)
Divisions :	Theses
Authors :	Name Email ORCID Scott, Andrew D.
Date :	2003
Contributors :	Contribution Name Email ORCID http://www.loc.gov/loc.terms/relators/THS
Depositing User :	EPrints Services
Date Deposited :	09 Nov 2017 12:16
Last Modified :	20 Jun 2018 11:17
URI:	http://epubs.surrey.ac.uk/id/eprint/844054

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