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Title: Livšic theorems and the stable ergodicity of compact group extensions for systems with some hyperbolicity
Author: Scott, Andrew D.
ISNI:       0000 0001 3557 351X
Awarding Body: University of Surrey
Current Institution: University of Surrey
Date of Award: 2003
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available