tommy's group addition isomo conjecture
#1
Let f(z) be an analytic function.

let z1 , z2 be complex numbers of the form a^2 + b^2 i  and c^2 + d^2 i 
such that Re ln(z1 + z2) =< ln (sqrt(2))

Let z_0 not be a fixpoint or cyclic point or singularity or pole of f(z).

and let f^[z1 + z2](z_0) = f^[w](z_0) = f^[z_1](f^[z_2](z_0)) =   f^[z_2](f^[z_1](z_0))

For all z1,z2 such that z1 + z2 = w.

Let s = g^2 + h^2 i
Also let f^[s](z_0) be injective for all complex 0 =< s =< w.

then 

f^[s](z_0) is analytic in s if 0 =< s =< w.

(the inequalities refer to the modulus comparisons)


Regards

tommy1729
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#2
related :

https://math.eretrandre.org/tetrationfor...p?tid=1639

https://math.eretrandre.org/tetrationfor...p?tid=1641
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