Laminations from the Main Cubioid

Abstract

According to a recent paper \cite{bopt13}, polynomials from the closure ${\overline{\mathrm{PHD}}}_3$ of the {\em Principal Hyperbolic Domain} ${\mathrm{PHD}}_3$ of the cubic connectedness locus have a few specific properties. The family $\mathrm{CU}$ of all polynomials with these properties is called the \emph{Main Cubioid}. In this paper we describe the set ${\mathrm{CU}}^c$ of laminations which can be associated to polynomials from $\mathrm{CU}$.

38 pages, 5 figures (in the new version a few typos have been corrected and a few proofs have been expanded). To appear in Discrete and Continuous Dynamical Systems. arXiv admin note: text overlap with arXiv:1106.5022