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arXiv · 1305.5799

Quadratic-like dynamics of cubic polynomials

Alexander Blokh·Lex Oversteegen·Ross Ptacek·Vladlen Timorin
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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.

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Alexander Blokh, Lex Oversteegen, Ross Ptacek, Vladlen Timorin. 2015-12-03. Quadratic-like dynamics of cubic polynomials. https://doi.org/10.1007/s00220-015-2559-6

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