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## Quadratic-like dynamics of cubic polynomials

Communications in Mathematical Physics. 2016. Vol. 341. No. 3. P. 733-749.
Blokh A., Oversteegen L., Ptacek R., Timorin V.

A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a nonrepelling 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.