The authors characterize, up to technical hypotheses, which moduli of continuity allow exceptional (Denjoy-type) C^{1,α} actions on the circle.
de la Harpe, T opics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000
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Integrability of moduli and regularity of Denjoy counterexamples
The authors characterize, up to technical hypotheses, which moduli of continuity allow exceptional (Denjoy-type) C^{1,α} actions on the circle.