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THE LIVSIC COCYCLE EQUATION FOR COMPACT LIE GROUP EXTENSIONS OF HYPERBOLIC SYSTEMS

Published online by Cambridge University Press:  01 October 1997

WILLIAM PARRY  and
MARK POLLICOTT
WILLIAM PARRY
Affiliation:
Department of Mathematics, Warwick University, Coventry CV4 7AL
MARK POLLICOTT
Affiliation:
Department of Mathematics, Warwick University, Coventry CV4 7AL
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Abstract

In this article we extend well-known results of Livsic on the regularity of measurable solutions to the cocycle equation. Livsic proved a regularity result for real valued cocycles, but for compact Lie group valued cocycles his result was restricted to coboundaries (that is, trivial or constant cocycles). In this article we prove the complete result.

We present several useful applications of these results.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 405 - 416
Copyright
The London Mathematical Society 1997

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