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Title

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

Authors 1

Affiliations

  1. Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Abstract

This is the first part of the work studying the family F of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of F and give a detailed study of the subfamily ℱ2 consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in ℱ2 from Newton maps to maps with so-called exotic basins.

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Fundamenta Mathematicae
1998/158/3
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Pages:
249-288
Main language of publication
English
Received
1997-12-01
Accepted
1998-07-07
Published
1998
Exact and natural sciences