Reading this wikipedia article on Julia sets. I'm curious about the proof that there exists a biholomorphic map $\psi$ from the Fatou set of $z^2+c$, where $c$ is in the Mandelbrot set, to the exterior of the unit circle. If you don't know the proof do you know where I could learn about it? The sources cited in that section of the article are an $80 book and a paper by Douady and Hubbard in French.
2026-03-25 22:05:36.1774476336
Proof that there is a biholomorphic map from a Fatou set to the exterior of the unit circle?
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I found this website look here :https://en.m.wikipedia.org/wiki/Riemann_mapping_theorem
You should search Riemann mapping proof and then put your specific conditions. Look here also http://www.gvp.cz/~vinkle/mafynet/GeoGebra/matematika/fraktaly../linearni_system/julia.pdf
This book might interest you https://www.amazon.com/Mandelbrot-Julia-Sets-Dynamics-Activities/dp/1559533579
You might want to start with Beniot Mandelbrot's own fractal Geometry of Nature (textbook). Search Julia sets there are so many PDF's on it.
This website has lots of info on Julia sets http://ibiblio.org/e-notes/MSet/Contents.htm And this one too https://www.cut-the-knot.org/Curriculum/Algebra/JuliaIndexing.shtml
$$Eureka!$$ This talks about your problem specifically https://www.mcgoodwin.net/julia/juliajewels.html