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On holomorphic critical quasi-circle maps

Published online by Cambridge University Press:  18 October 2004

CARSTEN LUNDE PETERSEN
CARSTEN LUNDE PETERSEN
Affiliation:
IMFUFA, Roskilde University, DK-4000 Roskilde, Denmark
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Abstract

The so-called Herman–Światek theorem is generalized to holomorphic self-homeomorphisms of quasi-circles. This result implies an unpublished theorem of Michel Herman: If a Siegel disk or Arnold–Herman ring for a rational map has a boundary component, which is a quasi-circle containing a critical point, then the associated rotation number is Diophantine of exponent 2.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 5 , October 2004 , pp. 1739 - 1751
Copyright
© 2004 Cambridge University Press

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