Julia sets in parameter spaces
type: Item
instance of: scholarly article
title: Julia sets in parameter spaces
zbMATH Open document ID: 0991.37029
DOI: 10.1007/PL00005568
author: Xavier Buff
author: Christian Henriksen
published in: Communications in Mathematical Physics
publication date: 2002-01-27T00:00:00Z
review text: The paper is devoted to study the one parameter family of cubic polynomials \[ g_b(z)= \lambda z+ bz^2+z^3, \quad b\in \mathbb{C},\tag{1} \] where \(\lambda= e^{2\pi i\theta}\) is a fixed complex number of modulus 1. The authors show that the bifurcation locus of (1) contains quasi-conformal copies of the quadratic Julia set \(J(\lambda z+z^2)\). As a consequence, they show that when the Julia set \(J(\lambda z+z^2)\) is not locally connected, then the bifurcation locus is not locally connected. The proofs use results of Douady-Hubbard [see \textit{A. Douady} and \textit{J. H. Hubbard}, C. R. Acad. Sci., Paris, Sér. I 294, 123-126 (1982; Zbl 0483.30014)] and Branner-Hubbard [\textit{B. Branner} and \textit{J. H. Hubbard}, Acta Math. 160, 143-206 (1988; Zbl 0668.30008)].
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 37F45
zbMATH DE Number: 1695547
zbMATH Keywords: connectedness
zbMATH Keywords: Julia set
zbMATH Keywords: bifurcation locus
MaRDI profile type: Publication
Wikidata QID: Q56005163
full work available at URL: pl00005568
OpenAlex ID: W1989893661
description: scientific article; zbMATH DE number 1695547