On critical circle homeomorphisms

  • Grzegorz Światek


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.


Cross-ratio inequality quasi-symmetric conjugacy Denjoy theorem 


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Copyright information

© Sociedade Brasileira de Matemática 1998

Authors and Affiliations

  • Grzegorz Światek
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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