Self-overlays and symmetries of Julia sets of expanding maps
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.
scientific article; zbMATH DE number 6934068
scientific article