Symmetries of Julia sets of nondegenerate polynomial skew products on \(\mathbb{C}^{2}\)
type: Item
instance of: scholarly article
title: Symmetries of Julia sets of nondegenerate polynomial skew products on \(\mathbb{C}^{2}\)
zbMATH Open document ID: 1205.37059
author: Kohei Ueno
published in: Michigan Mathematical Journal
publication date: 2010-06-17T00:00:00Z
review text: The paper originates from the idea that the Julia sets of any kind of functions and maps can have symmetries. For the Julia set of a polynomial the symmetries are rotations. This problem being solved i.e. determination of the group of symmetries and of the polynomials having the same Julia set, the paper deals with the same problem in two dimensions. There are considered non-degenerate polynomials skew products in \(\mathbb{C}^2\), existence of vertical Green functions and Böttcher functions of the map, symmetries of the Julia set. It is then shown that the suitable transformations preserving the Julia set are conjugate to the rotational product map. A necessary and sufficient condition is given for the group of symmetries to be infinite.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 37F50
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 37C80
zbMATH DE Number: 5723344
zbMATH Keywords: Julia sets on \(\mathbb{C}^2\)
zbMATH Keywords: non-degenerate polynomials skew products
Wikidata QID: Q121770191
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1272376030
OpenAlex ID: W2048297251
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cites work: Dynamics of polynomial skew products on \(\mathbb{C}^2\)
cites work: The Polynomials Associated with a Julia Set
DOI: 10.1307/MMJ/1272376030
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description: scientific article; zbMATH DE number 5723344