Abstract
We prove that an analytic circle homeomorphism without periodic orbits is conjugated to the linear rotation by a quasi-symmetric map if an only if its rotation number is of constant type. Next, we consider automorphisms of quasi-conformal Jordan curves, without periodic orbits and holomorphic in a neighborhood. We prove a “Denjoy theorem” that such maps are conjugated to a rotation on the circle.
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Dedicated to the memory of R. Mañé
Partially supported by NSF grant DMS-9704368 and the Sloan Foundation.
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Światek, G. On critical circle homeomorphisms. Bol. Soc. Bras. Mat 29, 329–351 (1998). https://doi.org/10.1007/BF01237654
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DOI: https://doi.org/10.1007/BF01237654