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How regular can the boundary of a quadratic Siegel disk be?
Author(s):
Xavier
Buff;
Arnaud
Chéritat
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1073-1080.
MSC (2000):
Primary 37F50, 37F10, 46B50
Posted:
September 26, 2006
MathSciNet review:
2262908
Retrieve article in:
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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  but not  Jordan curves.
References:
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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:
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
Posted:
September 26, 2006
Communicated by:
Linda Keen
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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