Some "Theorem" on the generalized superfunction

[Leo.W]

One of sheldon's posts mentioned Peter Walker's 1991 paper

https://math.eretrandre.org/tetrationfor...p?tid=1292
In which he discribed a function to connect the natural tetration and the generalized iteration of f(z)=exp(z)-1
The method is the same to Cancel Law(f(z)=z+1,g(z)=exp(z)-1,h(z)=exp(z))

Most generalized iteration for some functions having no finite fixed point, like
f(z)=2sinh(ln(z)) https://math.eretrandre.org/tetrationfor...p?tid=1305
f(z)=z+z^-1
f(z)=2z+z^-1
f(z)=z+exp(z)
f(z)=z+ln(z)
we can use the transformation of the fixed points (or conjugacy):
f(z)=2sinh(ln(z))   q(z)=z^-1   F(z)=q(f(q^-1(z)))=-1/2csch(ln(z)) having parabolic fixed point 0
f(z)=z+z^-1   q(z)=z^-1   F(z)=q(f(q^-1(z)))=z/(z^2+1) having parabolic fixed point 0
f(z)=2z+z^-1   q(z)=z^-1   F(z)=q(f(q^-1(z)))=z/(z^2+2) having elliptic(attracting) fixed point 0
f(z)=z+exp(z)   q(z)=exp(z)   F(z)=q(f(q^-1(z)))=z*exp(z) having parabolic fixed point 0
f(z)=z+ln(z)   q(z)=exp(z)   F(z)=q(f(q^-1(z)))=ln(z+exp(z)) having parabolic fixed point 0
Then we generate F^t(z) and plug it into f^t(z)=q^-1(F^t(q(z)))