Laminations from the Main Cubioid

Alexander Blokh; Lex Oversteegen; Ross Ptacek; Vladlen Timorin

Laminations from the Main Cubioid

Dynamical Systems 2019-04-01 v3

Authors: Alexander Blokh , Lex Oversteegen , Ross Ptacek , Vladlen Timorin

Abstract

According to a recent paper \cite{bopt13}, polynomials from the closure $\bar{\rm PHD}_3$ of the {\em Principal Hyperbolic Domain} ${\rm PHD}_3$ 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 $\mathrm{CU}$ .

Cite

@article{arxiv.1305.5788,
  title  = {Laminations from the Main Cubioid},
  author = {Alexander Blokh and Lex Oversteegen and Ross Ptacek and Vladlen Timorin},
  journal= {arXiv preprint arXiv:1305.5788},
  year   = {2019}
}

Comments

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

Laminations from the Main Cubioid

Abstract

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