Maybe the solution at z=0 to f(f(z))=-z+z^2

[tommy1729]

Dear Leo

It might make more sense using series expansions derived from asymptotics.

This usually improves convergeance and analyticity.

And adding some fractal structure  :


f(f(z))= - z + z^2

f(z) = G_1(G_2(z))

G_1(z) = sqrt(i) z + a z^(1/sqrt(2)) + b z^(sqrt(2)-1) + c z^((1/sqrt(2))+1)  + d x^2 + ...

G_2(z) = sqrt(i) z + a_2 z^(1/sqrt(2)) + b_2 z^(sqrt(2)-1) + c_2 z^((1/sqrt(2))+1)  + d_2 x^2 + ...

for some real a,b,c,d,a_2,b_2,c_2,d_2 or more if you want.


regards

tommy1729