Herman's condition and critical points on the boundary of Siegel disks of polynomials with two critical values

Abstract

We extend a theorem of Herman from the case of unicritical polynomials to the case of polynomials with two finite critical values. This theorem states that Siegel disks of such polynomials, under a diophantine condition (called Herman's condition) on the rotation number, must have a critical point on their boundaries.

arXiv comment28 pages. The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-016-2614-y

References in corpus (1)

• Polynomial Siegel disks are typically Jordan domains

Cited by in corpus (3)

• The high type quadratic Siegel disks are Jordan domains
• The size of quadratic $p$-adic linearization disks
• Siegel disks of the tangent family