From Newton’s method to exotic basins Part I: The parameter space

Volume 158 / 1998

Krzysztof Barański 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.

Authors

  • Krzysztof Barański

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