From Newton’s method to exotic basins Part I: The parameter space
Volume 158 / 1998
Fundamenta Mathematicae 158 (1998), 249-288
DOI: 10.4064/fm-158-3-249-288
Abstract
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.
