If $|t| = |W(-\ln z)| = 1$ and $t^n =1$ then $z^{z^{z^{...}}}$ is convergent

Question

Let $z \in \mathbb{C}$ and $W$ be the Lambert W function. In this post I was told if $|t| = |W(-\ln z)| = 1$ and $t^n =1$ for some $n \in \mathbb{N}$ than the iterated exponential $z^{z^{z^{...}}}$ is convergent, and that this is proved by Baker and Rippon. However, I have found that the relevant article is not freely available.

I am asking for a link to an article, possibly by a different author, which proves this or an equivalent statement. Preferably, the article should be freely available, no questions asked.

@JackD'Aurizio Thank you very much. I have been trying to get my hands on that article for several days. — cpiegore, Jun 14 '16 at 21:16

score 1 · Accepted Answer · answered Jun 16 '16 at 06:21

Just to make it possible to "close the case": The article is possibly

Baker, I. N., and Rippon P. J. "A Note on Complex Iteration." The American Mathematical Monthly 92.7 (1985): 501-04. Web.

This is online, for instance via JStor. (Access possible using an account of an affiliated university or organiszation)

If $|t| = |W(-\ln z)| = 1$ and $t^n =1$ then $z^{z^{z^{...}}}$ is convergent

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