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Livšic theorems and stable ergodicity for group extensions of hyperbolic systems with discontinuities

Published online by Cambridge University Press:  02 December 2003

MATTHEW NICOL and
ANDREW SCOTT
MATTHEW NICOL
Affiliation:
Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK (e-mail: m.nicol@surrey.ac.uk, a.scott@surrey.ac.uk)
ANDREW SCOTT
Affiliation:
Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK (e-mail: m.nicol@surrey.ac.uk, a.scott@surrey.ac.uk)
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Abstract

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We prove measurable Livšic theorems for Lie group valued cocycles over certain classes of uniformly hyperbolic maps with discontinuities, in particular the $\beta$-transformation, C2 Markov maps and a simple class of toral linked twist maps. As an application, we establish stable ergodicity results for compact group extensions of certain classes of uniformly hyperbolic systems with discontinuities.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 6 , December 2003, pp. 1867 - 1889
Copyright
2003 Cambridge University Press