Capture components of cubic Siegel polynomials

Abstract

Let $\theta$ be an irrational number of bounded type. We prove that all capture components in the parameter space of cubic polynomials $f_a(z)=e^{2\pi i\theta }z+a{z}^2+z^3$, where $a\in \mathbb{C}$, are Jordan domains.

16 pages, 2 figures; to appear in Chinese Annals of Mathematics, Series B