English

Smooth Siegel disks without number theory: A remark on a proof by Buff and Cheritat

Dynamical Systems 2014-04-04 v1 Complex Variables

Abstract

X. Buff and A. Cheritat proved that there are quadratic polynomials having Siegel disks with smooth boundaries. Based on a simplification of A. Avila, we give yet another simplification of their proof. The main tool used is a harmonic function introduced by Yoccoz whose boundary values are the sizes of the Siegel disks. The proof also applies to some other families of polynomials, entire and meromorphic functions.

Keywords

Cite

@article{arxiv.math/0510578,
  title  = {Smooth Siegel disks without number theory: A remark on a proof by Buff and Cheritat},
  author = {Lukas Geyer},
  journal= {arXiv preprint arXiv:math/0510578},
  year   = {2014}
}

Comments

5 pages