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Constructing real tetration solutions - Printable Version

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Constructing real tetration solutions - Daniel - 12/22/2019

Has anyone considered using the countable complex fixed points to construct real tetrational solutions?


RE: Constructing real tetration solutions - bo198214 - 12/22/2019

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.


RE: Constructing real tetration solutions - Daniel - 12/23/2019

(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


RE: Constructing real tetration solutions - bo198214 - 12/23/2019

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.


RE: Constructing real tetration solutions - sheldonison - 12/24/2019

(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/tetrationforum/showthread.php?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.