UNSPECIFIED (1999) The Livsic periodic point theorem for non-abelian cocycles. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 19 (Part 3). pp. 687-701. ISSN 0143-3857

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Abstract

For hyperbolic systems and for Holder cocycles with values in a compact metric group, we extend Livsic's periodic point characterisation of coboundaries. Here we show that two such cocycles are cohomologous when their respective 'weights' (of closed orbits) coincide. When it is only assumed that they are conjugate, one of the cocycles must (in general) be modified by an isomorphism (which stabilises conjugacy classes) to obtain cohomology. When the group is Lie and when a transitivity condition is satisfied, conjugacy of weights ensures that the cocycles are cohomologous with respect to a finitely extended group.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ERGODIC THEORY AND DYNAMICAL SYSTEMS
Publisher:	CAMBRIDGE UNIV PRESS
ISSN:	0143-3857
Date:	June 1999
Volume:	19
Number:	Part 3
Number of Pages:	15
Page Range:	pp. 687-701
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/14429

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