Iteration with two analytic fixed points

[bo198214]

As to
MR0729400 S. Dubuc, Étude théorique et numérique de la fonction de Karlin-McGregor, J. Analyse Math. 42 (1982/83), 15–37.

I renewed my alumni library access, however they would not grant me online access to
https://link.springer.com/article/10.1007/BF02786869
(you know all this licensing stuff that would fill the pockets of the publishers)

So I had to walk the old fashioned way - to the journals in paper - and photographed the article.
Its in single pages - you could use something like google Lens to translate it into your native language.

However, after reading the article, it rather explaines why the differences between the regular iterates of real neighboring fixed points are so small, instead of giving an overview which functions have different iterates and which don't.

Here are the pages: