complex iteration (complex "height")

[Ivars]

Specialized to our case using the lower fixed point \( a \) we get the base by \( b=a^{1/a} \) and \( f'(a)=(b^x)'(a)=\ln(b)b^a=\ln(b)a=\ln(b^a)=\ln(a) \), so:

\( b[4]z=\exp_b^{\circ z}(1)=\lim_{n\to\infty} \log_b^{\circ n}(a(1-\ln(a)^z) + \ln(a)^z \exp_b^{\circ n}(1)) \)

Please just give still an explanation of what is this iteration -I am still not 100% sure I understand iteration symbols correctly.

\( \exp_b^{\circ n}(1)) \)

Thank you in advance,

Ivars