Mating non-renormalizable quadratic polynomials. (English) Zbl 1187.37065

Aspenberg, Magnus; Yampolsky, Michael

Commun. Math. Phys. 287, No. 1, 1-40 (2009).

Authors’ abstract: We prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of \({\mathcal M}\), is non-renormalizable, and does not have any non-repelling periodic orbits.

Reviewer: Viorel Vâjâitu (Bucureşti)

MSC:

37F10	Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37E15	Combinatorial dynamics (types of periodic orbits)
37F45	Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)

Keywords:

topological mating; conformal mating; Julia set; quadratic polynomial; irrational number of bounded type

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