08/23/2022, 11:52 AM
(08/23/2022, 05:13 AM)JmsNxn Wrote: (but you can apply it to \(\sqrt{2}\)).
Ok, I think that is where we stopped with your proof attempts ... for base \(\sqrt{2}\) one has as domain whole \(\mathbb{C}\).
And we know already by several means (one from Karlin&McGregor, but also because the multipliers are not reciprocal) that it can not have the same regular iteration at both fixed points, but maybe its still interesting to have another proof.
So here you have met all your assumptions, how would *your* proof go in this scanario (function is entire, domain is \(\mathbb{C}\))?
