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Livšic's theorem for semisimple Lie groups

Published online by Cambridge University Press:  08 October 2001

MATTHEW NICOL  and
MARK POLLICOTT
MATTHEW NICOL
Affiliation:
Department of Mathematics and Statistics, University of Surrey, Guildford GU2 7XH, UK
MARK POLLICOTT
Affiliation:
Mathematics Department, University of Manchester, Oxford Rd, Manchester M13 9PL, UK (e-mail: [email protected])
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Abstract

In this paper we show that strong generalizations of the measurable Livšic theorem for cocycles taking values in connected non-compact linear semisimple Lie groups, a canonical example being SL(2, \mathbb{R}), can be deduced from an elegant approach of Brin and Pesin to the dynamics of partially hyperbolic systems.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 5 , October 2001 , pp. 1501 - 1509
Copyright
2001 Cambridge University Press

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