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
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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 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
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.
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. 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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