07/13/2022, 08:49 PM
(07/13/2022, 08:32 PM)bo198214 Wrote: If there is a method to calculate f^a as a so called iteration semi group then there is already a proof that f^a o f^b = f^(a+b) because that's how an iteration semi group is defined, like it is for the Schroeder/regular iteration. So I really don't understand what sanity check you are after (that's why I said: make yourself familiar with the proofs). So I thought you meant some numerical verification. Seems you don't mean that but something symbolically - whatever that means.
And here I really ask you to be more specific, are we talking about the case b<=eta or b>eta (and please spare me to hear you considering general functions). For 1<b<eta we have the usual regular iteration at one of the two fixed points, and everything is proven and explored there (though to our dissatisfaction because there is not the one true solution) For b>eta we have a bunch of numerical methods (invented on this forum) for none of them even exists a proof of convergence - how do you want to check anything symbolically there?! And then we have the proven constructions by Kneser and Leau-Fatou which vice versa have no straight numerical implementation. So what do you want to check symbolically there? (Except RTFP - reading the fucking proof)
"Read the fucking proof?" Ciao baby, I'm permanently gone.
Daniel