Abstract
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 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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Blokh, A., Oversteegen, L., Ptacek, R. et al. Quadratic-Like Dynamics of Cubic Polynomials. Commun. Math. Phys. 341, 733–749 (2016). https://doi.org/10.1007/s00220-015-2559-6
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DOI: https://doi.org/10.1007/s00220-015-2559-6