02/09/2023, 05:20 AM
I didn't resist the effects of COVID19 as easily as I thought I would. I hope I didn't miss anything interesting.
Are there any noteworthy developments about tetration in the last six months?

02/09/2023, 05:20 AM
I didn't resist the effects of COVID19 as easily as I thought I would. I hope I didn't miss anything interesting.
I think the only real "tetrationy" stuff that has happened hereat least on mine and Gottfried's part has been discussing Neutral fixed points. Where we have stumbled across a bunch of literature which confirms that there is no holomorphic function:
\[ g(g(x)) = \eta^x\\ \] For \(x\) in a neighborhood of \(e\). And we were able to find proofs of very tight bounds on this series; where: \[ g(x) = e + \sum_{k=1}^\infty a_k (xe)^k\\ \] Where: \[ a_k = O(c^k k!) \] This led me to write a half finished paper, I should get back to, about iterating around neutral fixed points in general. It didn't really go anywhere though really. But we did cover a lot of ground on asymptotic series expansions near neutral fixed points; and their relation to Abel functions, so that's cool ! The rest of the stuff that's happened here has been the usual whacky "tetration adjacent" stuff, lol
02/11/2023, 08:34 PM
(02/10/2023, 03:27 AM)JmsNxn Wrote: I think the only real "tetrationy" stuff that has happened hereat least on mine and Gottfried's part has been discussing Neutral fixed points. Where we have stumbled across a bunch of literature which confirms that there is no holomorphic function: Fortunately, I really didn't miss much. And congratulations on your discovery. The neutral fixed points is quite mysterious, and it's a good thing to have more understanding. 
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