Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Natural cyclic superfunction
Natural cyclic superfunction are superfunction that naturally extend from integer iterates to real ones.


F(2x) = 2 F(x) sqrt( 1 - F(x)^2 ) = g(F(x)).

F(1) = sin(1) makes the solution natural : sin(x).


Funny thing is this is Well studied for the complex numbers.

We can probably learn from considering fractals and chaos on the complex plane and then take the real part ...

Mick has posted this on MSE and MO btw.
Maybe that Will help.

I lack time but intend to work and answer this !




Where our friend mick has posted the question on MSE.

Thanks mick.


In the first post I starters with a variant of the logistic map.
Guess that is obvious.

I started considering

F(2x) = g(F(x)).

Mick started with F(x+1) = g(F(x)).

2 forms of the same idea.

Just like fake function theory we can see this as an intresting regression problem.

Mick's latest post captures the idea very well !

Although a specific question, im confident an answer will provide the necc insights for many cases.



Possibly Related Threads…
Thread Author Replies Views Last Post
Question Natural Properties of the Tetra-Euler Number Catullus 6 354 07/01/2022, 08:16 AM
Last Post: Catullus
  Some "Theorem" on the generalized superfunction Leo.W 48 16,209 06/18/2022, 08:39 AM
Last Post: Leo.W
Question Iterated Hyperbolic Sine and Iterated Natural Logarithm Catullus 2 272 06/11/2022, 11:58 AM
Last Post: tommy1729
  Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 11,932 05/26/2021, 11:55 PM
Last Post: MphLee
  Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 3,606 09/09/2019, 10:50 PM
Last Post: tommy1729
  Polygon cyclic fixpoint conjecture tommy1729 1 4,989 05/18/2016, 12:26 PM
Last Post: tommy1729
  Cyclic dynamics f(-x) = T (f(x)) tommy1729 2 5,610 08/25/2015, 08:23 AM
Last Post: tommy1729
  [2014] Uniqueness of periodic superfunction tommy1729 0 3,857 11/09/2014, 10:20 PM
Last Post: tommy1729
  twice a superfunction tommy1729 5 11,077 03/26/2014, 03:34 PM
Last Post: MphLee
  The fermat superfunction tommy1729 3 7,243 03/24/2014, 12:58 AM
Last Post: tommy1729

Users browsing this thread: 1 Guest(s)