Siegel disks with smooth boundaries

By Artur Avila, Xavier Buff, Arnaud Chéritat. 2004

53 citations recorded by the source corpus.

We show the existence of angles α ∈ R/Z such that the quadratic polynomial Pα(z) = e2iπαz + z2 has a Siegel disk with C∞-smooth boundary. This result was first announced by R. Perez-Marco in 1993.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2aa1b7dc4c7fdb9c7a61f1a5e1491e857f6ac0a9

Citations in the corpus

• Quadratic Julia Sets with Positive Area (2006, unknown): “enough (for a proof, see for example in [ ABC ], proposition 2, the remark following proposition 2 and theorem 3). Note that Xn(ρ) ⊂ D(0, ρ) and the limit values of the sequence (χn : Dn → C) are isomorphisms χ : D → �. It follows that for n large enough, χn Xn(ρ) � ⊂ χn D(0, ρ) � ⊂ χ D(0, √ ρ) � ⊂ ”