• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Natural cyclic superfunction tommy1729 Ultimate Fellow Posts: 1,427 Threads: 347 Joined: Feb 2009 11/28/2015, 01:28 PM Natural cyclic superfunction are superfunction that naturally extend from integer iterates to real ones. Example F(2x) = 2 F(x) sqrt( 1 - F(x)^2 ) = g(F(x)). F(1) = sin(1) makes the solution natural : sin(x). Regards Tommy1729 tommy1729 Ultimate Fellow Posts: 1,427 Threads: 347 Joined: Feb 2009 12/01/2015, 01:26 PM 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 ! Optimistic. Regards Tommy1729 tommy1729 Ultimate Fellow Posts: 1,427 Threads: 347 Joined: Feb 2009 12/02/2015, 10:27 PM See http://math.stackexchange.com/questions/...nal-period Where our friend mick has posted the question on MSE. Thanks mick. Regards Tommy1729 tommy1729 Ultimate Fellow Posts: 1,427 Threads: 347 Joined: Feb 2009 12/08/2015, 12:09 AM 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 ! http://math.stackexchange.com/questions/...-a-n-a-n-1 Although a specific question, im confident an answer will provide the necc insights for many cases. Regards Tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Some "Theorem" on the generalized superfunction Leo.W 21 650 05/11/2021, 08:41 PM Last Post: MphLee Generalized Kneser superfunction trick (the iterated limit definition) MphLee 21 2,775 03/29/2021, 02:54 AM Last Post: JmsNxn Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 2,373 09/09/2019, 10:50 PM Last Post: tommy1729 Polygon cyclic fixpoint conjecture tommy1729 1 3,759 05/18/2016, 12:26 PM Last Post: tommy1729 Cyclic dynamics f(-x) = T (f(x)) tommy1729 2 4,385 08/25/2015, 08:23 AM Last Post: tommy1729 [2014] Uniqueness of periodic superfunction tommy1729 0 3,019 11/09/2014, 10:20 PM Last Post: tommy1729 twice a superfunction tommy1729 5 8,775 03/26/2014, 03:34 PM Last Post: MphLee The fermat superfunction tommy1729 3 5,791 03/24/2014, 12:58 AM Last Post: tommy1729 Uniqueness of Ansus' extended sum superfunction bo198214 4 9,833 10/25/2013, 11:27 PM Last Post: tommy1729 2*sinh(3^h*asinh(x/2)) is the superfunction of (...) ? Gottfried 5 9,047 09/11/2013, 08:32 PM Last Post: Gottfried

Users browsing this thread: 1 Guest(s)