How regular can the boundary of a quadratic Siegel disk be?
Résumé
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.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)