Constructing real tetration solutions
#1
Has anyone considered using the countable complex fixed points to construct real tetrational solutions?
Daniel
#2
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.
#3
(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
#4
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.
#5
(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.
- Sheldon


Possibly Related Threads…
Thread Author Replies Views Last Post
  Behaviour of tetration into the real negatives Shanghai46 1 578 10/12/2023, 11:01 PM
Last Post: leon
  Real tetration as a limit of complex tetration Daniel 6 1,555 10/10/2023, 03:23 PM
Last Post: leon
  Real and complex tetration Daniel 13 4,119 04/04/2023, 10:25 AM
Last Post: JmsNxn
  Range of complex tetration as real Daniel 2 1,322 10/22/2022, 08:08 PM
Last Post: Shanghai46
  From complex to real tetration Daniel 3 1,586 10/21/2022, 07:55 PM
Last Post: Daniel
  Cost of real tetration Daniel 1 1,046 09/30/2022, 04:41 PM
Last Post: bo198214
  Real Multivalued/Parametrized Iteration Groups bo198214 11 3,905 09/10/2022, 11:56 AM
Last Post: tommy1729
  Constructive real tetration Daniel 1 975 09/01/2022, 05:41 AM
Last Post: JmsNxn
  Complex to real tetration Daniel 1 989 08/14/2022, 04:18 AM
Last Post: JmsNxn
  Constructing a real valued Fibonacci iteration--its relation to \(1/1+z\) JmsNxn 7 2,648 08/13/2022, 12:05 AM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)