The Livsic periodic point theorem for non-abelian cocycles
UNSPECIFIED (1999) The Livsic periodic point theorem for non-abelian cocycles. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 19 (Part 3). pp. 687-701. ISSN 0143-3857Full text not available from this repository.
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|
|Number of Pages:||15|
|Page Range:||pp. 687-701|
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