eta as branchpoint of tetrational

[bo198214]

So we somehow need to verify your assumption, that it converges to the upper fixpoint for positive imaginary infinity. Perhaps I will write a Wiki article about perturbed Fatou coordinates, which may help to decide this question.

So, I just finished writing up, whats in the article of Shishikura.
So far only quotes, its quite difficult, but I hope you see that he talks about the same thing we do.
You find it here on the Hyperoperations Wiki.
His \( f_0 \) corresponds to our \( \exp_\eta \).
His \( f \) (which corresponds to our \( \exp_{\eta+\eps} \)) has not two conjugate fixpoints, but one at 0 and one near zero.
His function \( \varphi_f \) corresponds to our superfunction.
And his function \( \tilde{\mathcal{R}} \) corresponds to our 1-periodic \( \theta \).
You can use the "Discussion" page whenever there something needs clarification.