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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
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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?)

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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: https://doi.org/10.1090/S0002-9939-06-08578-9
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.