Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society

, Volume 29, Issue 2, pp 329–351

On critical circle homeomorphisms

Authors

  • Grzegorz Światek
    • Department of MathematicsPennsylvania State University
Article

DOI: 10.1007/BF01237654

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

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.

Keywords

Cross-ratio inequalityquasi-symmetric conjugacyDenjoy theorem

Copyright information

© Sociedade Brasileira de Matemática 1998