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Working paper

Quadratic-like dynamics of cubic polynomials

arxiv.org. math. Cornell University, 2013. No. 1305.5799.
Timorin V., Blokh A., Oversteegen L., Ptacek R. M.
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.