There's a theorem that if all the orbits of the critical points of a complex polynomial map are bounded, the corresponding Julia set is connected. Also, if all the critical orbits escape to infinity, the Julia set is a cantor set. Where can I find a proof of this theorem? I have tried to find it but I cannot.
2026-03-26 23:10:42.1774566642
Where to find a proof of the Julia-Fatou theorem for the connectedness of Julia sets?
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Milnor's book, Dynamics in one complex variable, contains this theorem on page 96: