Quadratic-like dynamics of cubic polynomials
Abstract
A small perturbation of a quadratic polynomial with a non-repelling fixed point gives a polynomial with an attracting fixed point and a Jordan curve Julia set, on which the perturbed polynomial acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.
Keywords
Cite
@article{arxiv.1305.5799,
title = {Quadratic-like dynamics of cubic polynomials},
author = {Alexander Blokh and Lex Oversteegen and Ross Ptacek and Vladlen Timorin},
journal= {arXiv preprint arXiv:1305.5799},
year = {2016}
}
Comments
Now 23 pages. In the new version we strengthen some of the results using new arguments. We also expand some proofs and add some references. A preprint "Complementary components to the cubic Principal Hyperbolic Domain" with related results is being posted to arxiv too. The paper is to appear at Communications in Mathematical Physics