Eigensystem of tetration-matrices

[Gottfried]

I think what you have done is similar what I describe now:

[snip]
I think this completes the correspondences.

Henryk -
this again is a super entry for my personal dictionary :-) . It helps to let thoughts converge. I also read the article of Aldrovandi & Freitas about iteration (which Daniel mentioned earlier) meanwhile and I also am beginning to see the relations between the concepts from there. I'll post the last step, how I derived the X-matrix, later today; I think it'll come out as another simple translation of formalisms.

I'll try to find an answer for the last remark of your post:

Unfortunately this decomposition works merely if the function under consideration has a fixed point. In so far it is very interesting that it also converges for the non-fixed point case with base \( b>e^{1/e} \).

Thanks again -

Gottfried