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1998 | 158 | 3 | 249-288
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From Newton’s method to exotic basins Part I: The parameter space

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This is the first part of the work studying the family $\mathfrak{F}$ of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of $\mathfrak{F}$ and give a detailed study of the subfamily $ℱ_2$ consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in $ℱ_2$ from Newton maps to maps with so-called exotic basins.
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