12/22/2019, 10:53 AM

12/22/2019, 10:28 PM

Yes, Daniel that's the Kneser-Solution and many of the other methods discussed here are real-analytic solutions based on the primary complex fixed points.

12/23/2019, 02:52 AM

(12/22/2019, 10:28 PM)bo198214 Wrote: [ -> ]Yes, Daniel that's the Kneser-Solution and many of the other methods discussed here are real-analytic solutions based on the primary complex fixed points.

Yes, I'm now familiar with Kneser's approach thanks to your exposition of his work. I was thinking in terms of a countable number of fixed points, but given Kneser's work my requirement might be overkill.

Daniel

12/23/2019, 03:56 PM

As far as I know nobody managed to use any other fixpoint-pair than the primary one.

To use all the fixpoints seems to be a much stronger demand.

To use all the fixpoints seems to be a much stronger demand.

12/24/2019, 12:10 AM

(12/23/2019, 03:56 PM)bo198214 Wrote: [ -> ]As far as I know nobody managed to use any other fixpoint-pair than the primary one.

To use all the fixpoints seems to be a much stronger demand.

Daniel, Jay,

Please see this thread https://math.eretrandre.org/tetrationfor...hp?tid=452

About a year and half later, post#18, I generated a tetration solution from the secondary fixed point with the caveat that the derivative at the real axis goes to zero; see post#18; #19 in the thread I just linked to.

That solution has f' and f'' and tet(-1)=0; one can imagine that perhaps with the next fixed point pair, perhaps tet',tet'',tet''',tet'''' would all need to be zero .... I haven't revisited this post since 2011.