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irrational iterate of 2z(1-z)
#1
From examining the superfunction for 4z(1-z) about z=0, (one of the few elementary examples for a non-Mobius function), we get:


So [one of] the iterate of is . Putting these functions into the "Mandlebrot" form by conjugating with , we get that the iterate of is .

I was hoping to include some pictures of the Julia sets of these two functions, but I don't have ready access to a program that can draw general cubic sets (such as the old Autodesk Chaos program). So I'll try again in the morning, using Fractint.
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Messages In This Thread
irrational iterate of 2z(1-z) - by BenStandeven - 08/13/2010, 06:47 AM
RE: irrational iterate of 2z(1-z) - by tommy1729 - 08/09/2014, 10:16 PM

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