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LIVšIC REGULARITY THEOREMS FOR TWISTED COCYCLE EQUATIONS OVER HYPERBOLIC SYSTEMS
Published online by Cambridge University Press: 01 February 2000
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).
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- The London Mathematical Society 2000
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