Abstract
Cubic Newton 's methods are rational maps having three distinct super-attracting fixed points and a single free critical point. They form, up to conjugation, a family N λ parametrized by Λ = ℂ\\{0,±3/2}, and we denote by ℋ 0 the set of λ for which the free critical point of N λ is in the immediate basin of one of the super-attracting fixed points. In this Note, we show that the boundary of each connected component of ℋ 0 is a Jordan curve. For this, we determine in Λ regions on which the dynamics of N λ can be described by a fixed combinatorial model.
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