Hostname: page-component-5b777bbd6c-f9nfp Total loading time: 0 Render date: 2025-06-20T07:18:14.272Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 This result implies an unpublished theorem of Michel Herman: If a Siegel disk or Arnold–Herman ring for a rational map has a boundary component, which is a quasi-circle containing a critical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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable