I wrote some stuff on power series related to fractional iteration of functions (like solving f(f(x))=sin x) http://blog.sigfpe.com/2017/02/logarithms-and-exponentials-of-functions.html …
Can you write a closed form expression for the nth iteration of Mandelbrot's f(z)=z^2+c?
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Unfortunately I only deal with easy case f(z)=z+... Seen papers where inferences about Mandelbrot derived from simple case.
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I figured out the case derived from cos(2^n arccos(x)) long ago but couldn't progress further. Surely there's a generalization.
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