Self-overlays and symmetries of Julia sets of expanding maps
type: Item
instance of: scholarly article
title: Self-overlays and symmetries of Julia sets of expanding maps
zbMATH Open document ID: 1415.57003
author: José Ignacio Extremiana Aldana
author: L. Javier Hernández
author: Maria Teresa Rivas Rodriguez
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2018-09-07T00:00:00Z
review text: Given a compact Riemannian surface $M$ the authors of the paper under review do a computational study of the dynamics induced by a branched covering $f:M\rightarrow M$ considering shape and overlay theories. In this sense they have developed and implemented algorithms that give a shape resolution of the Julia set $J(f)$ when $f$ is an expanding map. Such a shape resolution is given by a certain inverse system of cubic complexes that are constructed using the notion of global multiplier. Then they are able to obtain visualizations of the fractal structure of the Julia set determining at the same time its shape. Considering the restriction map $f\vert_{J(f)}:J(f)\rightarrow J(f)$ they also give an overlay structure which contains many symmetry properties of the fractal structure of $J(f).$ As an example of their techniques they do an algorithmic study of branched self-coverings of the sphere.
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 54C56
Mathematics Subject Classification ID: 37F50
zbMATH DE Number: 6934068
zbMATH Keywords: overlay
zbMATH Keywords: Julia set
zbMATH Keywords: fundamental pro-groupoid
zbMATH Keywords: fundamental shape group
zbMATH Keywords: iterated subdivision
zbMATH Keywords: rational map
zbMATH Keywords: global multiplier
reviewed by: José Calcines
MaRDI profile type: Publication
full work available at URL: s13398-018-0501-4
OpenAlex ID: W2788104231
Wikidata QID: Q122712413
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DOI: 10.1007/S13398-018-0501-4
description: scientific article; zbMATH DE number 6934068