A model of the cubic connectedness locus
Dynamical Systems
2025-06-17 v2
Abstract
We describe a locally connected model of the boundary of the cubic connectedness locus. The model is obtained by constructing a decomposition of the space of critical portraits and collapsing elements of the decomposition into points. This model is similar to a quotient of the quadratic combinatorial locus where all baby Mandelbrot sets are collapsed to points. All fibers of the model, possibly except one, are connected. This paper is dedicated to the memory of Yuri Ilyich Lyubich.
Cite
@article{arxiv.2304.11516,
title = {A model of the cubic connectedness locus},
author = {Alexander Blokh and Lex Oversteegen and Vladlen Timorin and Yimin Wang},
journal= {arXiv preprint arXiv:2304.11516},
year = {2025}
}
Comments
47 pages, 2 figures