Bounded critical Fatou components are Jordan domains, for polynomials

TL;DR

This paper proves that for polynomials, the boundary of any bounded Fatou component is a Jordan curve, with the possible exception of Siegel disks, advancing understanding of complex dynamics boundaries.

Contribution

It establishes that bounded Fatou components are Jordan domains for polynomials, except potentially for Siegel disks, clarifying boundary regularity in complex dynamics.

Findings

Bounded Fatou component boundaries are Jordan curves.

Siegel disks may be exceptions.

Advances understanding of polynomial dynamics boundaries.

Abstract

We prove that, for polynomials, the boundary of any bounded Fatou component is a Jordan curve, except maybe for Siegel disks.