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 Merged fixpoints of 2 iterates ? Asymptotic ? [2019] tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 09/09/2019, 11:29 PM (This post was last modified: 09/09/2019, 11:39 PM by tommy1729.) Consider the function f(z) = exp(z) + z. f(z) has no finite fixpoints. We do iterates ( fractional near the real line ) by moving the fixpoint at oo to a finite place.  Of other ways. I Came to consider the following f^[2](z) = exp(exp(z)) exp(z) + exp(z) + z. The finite fixpoints are then  Exp(z) ( exp(exp(z)) +1 )  + z = z => Exp(z) ( exp(exp(z)) + 1) = 0 =>  Z = ln( ln(-1) )  One solution is  ln( pi ) + pi / 2 i = A And another the complex conjugate of A : B. Now i wonder if we take the half- iterates of f^[2] from those 2 fixpoints ( A and B ) based on koenigs solutions , Call them  FA(z) and FB(z). And then take the average of them :  C(z) = ( FA(z) + FB(z))/2   [ i call this merged fixpoints method ] Then is C(x) , where x is real , close to f(x) ?? And how does C(z) behave on the complex plane ? ---- Similar questions for the merged fixpoints of g(z,t) = (z^2 + t) + z with t ≥ 1. Notice g has only 2 fixpoints. Plots would be nice too. Regards Tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Merged fixpoints of 2 iterates ? Asymptotic ? [2019] - by tommy1729 - 09/09/2019, 11:29 PM RE: Merged fixpoints of 2 iterates ? Asymptotic ? [2019] - by sheldonison - 09/10/2019, 11:28 AM

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