How regular can the boundary of a quadratic Siegel disk be?
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- by Xavier Buff and Arnaud Chéritat PDF
- Proc. Amer. Math. Soc. 135 (2007), 1073-1080 Request permission
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
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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
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1073-1080
- MSC (2000): Primary 37F50, 37F10, 46B50
- DOI: https://doi.org/10.1090/S0002-9939-06-08578-9
- MathSciNet review: 2262908