12/22/2019, 10:53 AM
Has anyone considered using the countable complex fixed points to construct real tetrational solutions?
Daniel
Constructing real tetration solutions

12/22/2019, 10:53 AM
Has anyone considered using the countable complex fixed points to construct real tetrational solutions?
Daniel
12/22/2019, 10:28 PM
Yes, Daniel that's the KneserSolution and many of the other methods discussed here are realanalytic 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 KneserSolution and many of the other methods discussed here are realanalytic 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
Daniel
12/23/2019, 03:56 PM
As far as I know nobody managed to use any other fixpointpair than the primary one.
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 fixpointpair than the primary one. 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.
 Sheldon

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