the inconsistency depending on fixpoint-selection

[Gottfried]

Hey Gottfried, it is a quite well known result, that in most cases the regular iteration of an analytic function at different fixed points gives different (usually only slightly differing) functions. Ecalle referred me even to an article about this phenomenon

"Etude theorique et numerique de la fonction de Karlin-McGregor",
Serge Dubuc, Journal d'Analyse Math.. Vol. 42 (1982 / 83)

Is this also available in english? (I don't speak french... )
Well, it should be not too difficult to construct examples...

and I checked it numerically in the bummer thread.

...as you did it. But I didn't recognize a final conclusion, usable for our case. Damn, I've much too little experience...

So this requires more reading and testing first. Thanks for the hints!

Gottfried