Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

How regular can the boundary of a quadratic Siegel disk be?


Authors: Xavier Buff and Arnaud Chéritat
Journal: Proc. Amer. Math. Soc. 135 (2007), 1073-1080
MSC (2000): Primary 37F50, 37F10, 46B50
Published electronically: September 26, 2006
MathSciNet review: 2262908
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the family of quadratic polynomials with an irrationally indifferent fixed point, we show the existence of Siegel disks with a fine control on the degree of regularity of the linearizing map on their boundary. A general theorem is stated and proved. As a particular case, we show that in the quadratic family, there are Siegel disks whose boundaries are $ C^n$ but not $ C^{n+1}$ Jordan curves.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37F50, 37F10, 46B50

Retrieve articles in all journals with MSC (2000): 37F50, 37F10, 46B50


Additional Information

Xavier Buff
Affiliation: Université Paul Sabatier, Laboratoire Emile Picard, 118, route de Narbonne, 31062 Toulouse Cedex, France
Email: buff@picard.ups-tlse.fr

Arnaud Chéritat
Affiliation: Université Paul Sabatier, Laboratoire Emile Picard, 118, route de Narbonne, 31062 Toulouse Cedex, France
Email: cheritat@picard.ups-tlse.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08578-9
PII: S 0002-9939(06)08578-9
Received by editor(s): January 28, 2005
Received by editor(s) in revised form: November 2, 2005
Published electronically: September 26, 2006
Communicated by: Linda Keen
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.