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LIVšIC REGULARITY THEOREMS FOR TWISTED COCYCLE EQUATIONS OVER HYPERBOLIC SYSTEMS

Published online by Cambridge University Press:  01 February 2000

C. P. WALKDEN
C. P. WALKDEN
Affiliation:
Department of Mathematics, Manchester University, Oxford Road, Manchester M13 9PL, UK; cwalkden@ma.man.ac.uk
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Abstract

Let ϕ be a hyperbolic map. Cocycle equations of the form f = uϕ·g·αu−1 are considered, with f, g, u taking values in a compact connected Lie group G, α being an automorphism of G and f, g being Hölder continuous. When the eigenvalues of the derivative of α have modulus 1, it is proved that any measurable solution u has a Hölder continuous version. This condition on α is optimal. When f, g are Ck then u may be taken to be Ck−1+ε for any ε ∈ (0, 1).

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 61 , Issue 1 , February 2000 , pp. 286 - 300
Copyright
The London Mathematical Society 2000

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