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Systems Mid‑importance This article is within the scope of WikiProject Systems, which collaborates on articles related to systems and systems science.SystemsWikipedia:WikiProject SystemsTemplate:WikiProject SystemsSystems articles Mid This article has been rated as Mid-importance on the project's importance scale. This article is within the field of Dynamical systems.

Im not really great yet with the wiki syntax, but I belive that this theorem is very important in this field, and is one of the most important proofs in complex dynamics. Paxinum 20:35, 1 March 2007 (UTC) reply

OK, but the mathematician who proved it (Dennis Sulivan) already had a wikipedia article. So I put the link to that page, and added some relevant info. I will also redirect the D. Sullivan page to Dennis Sullivan, and move the content there. Hope this will do it. Turgidson 03:05, 2 March 2007 (UTC) reply

I realized that U must be a component of the Fatou set, but I have trouble finding a precise definition; Complex Dynamics by Carleson & Gamelin have the full proof of the theorem, but I have trouble finding the definition of component, which is one reason that I started this article, I wanted to know how to propely use it.

Oh, and I would like to use ${\displaystyle f_{k}}$ instead of ${\displaystyle f^{k}}$, this is the notation used in Iteration of Rational Functions, by Beardon, and in Complex dynamics. The reason is that the derivative ${\displaystyle f'_{k}}$ is easier to denote with subscripted k.

Paxinum 17:01, 2 March 2007 (UTC) reply

Fair enough (about the notation), especially since you have now explained it. -- Jitse Niesen ( talk) 03:14, 3 March 2007 (UTC) reply

The caption on the image shown reads like this: "This image illustrates the dynamics of ; the Fatou set (consisting entirely of wandering domains) is shown in white, while the Julia set is shown in tones of gray."

The dynamics of what??? I don't think anything is wrong with the sentence structure or the punctuation; there's just a missing word right before the semicolon. I'd fill it in, except I have no idea what it should be. 2600:6C50:800:2787:4544:D3E8:A5C4:D2D0 ( talk) 16:11, 26 March 2022 (UTC) reply