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arXiv:1305.5799 [math.DS]AbstractReferencesReviewsResources

Quadratic-like dynamics of cubic polynomials

Alexander Blokh, Lex Oversteegen, Ross Ptacek, Vladlen Timorin

Published 2013-05-24, updated 2014-11-10Version 2

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.

Comments: 21 pages. In the new version we strengthen some of the results using new arguments. A preprint "Complementary components to the cubic Principal Hyperbolic Domain" with related results is being posted to arxiv too
Categories: math.DS
Subjects: 37F45, 37F10, 37F20, 37F50
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