On critical circle homeomorphisms
- Cite this article as:
- Światek, G. Bol. Soc. Bras. Mat (1998) 29: 329. doi:10.1007/BF01237654
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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.