• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 2 fixpoint pairs [2015] tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 02/18/2015, 11:29 PM A general question. Let A(z) be a transcendental real-entire function without real fixpoints. Let I(z) be the functional inverse of A(z). I(z) has no singularities for Re(z) > 0. I(z) = z has exactly 2 conjugate pair solutions. The fixpoints of I(z) are all repelling and have real part > 0. Also they have the same derivative. (up to conjugate) Then by using the Kneser method we can find 2 real-analytic superfunctions based on one of the fixpoint pairs of I(z). By using analytic one-periodic theta functions we can modify those 2 superfunctions such that they are bounded in the strip 0 < Re(z) < 1. Call these real-analytic superfunctions F(z) and G(z). Consider D = lim F(z-n)/G(z-n) Im intrested in the behaviour of F(z) / ( D G(z) ) - 1 in the complex plane. regards tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Iteration exercises: f(x)=x^2 - 0.5 ; Fixpoint-irritation... Gottfried 23 53,319 10/20/2017, 08:32 PM Last Post: Gottfried (Again) fixpoint outside Period tommy1729 2 5,577 02/05/2017, 09:42 AM Last Post: tommy1729 Polygon cyclic fixpoint conjecture tommy1729 1 4,573 05/18/2016, 12:26 PM Last Post: tommy1729 The " outside " fixpoint ? tommy1729 0 2,945 03/18/2016, 01:16 PM Last Post: tommy1729 2015 Continuum sum conjecture tommy1729 3 6,877 05/26/2015, 12:24 PM Last Post: tommy1729 [2015] Spiderweb theory tommy1729 0 3,381 03/29/2015, 06:25 PM Last Post: tommy1729 [2015] 4th Zeration from base change pentation tommy1729 5 11,376 03/29/2015, 05:47 PM Last Post: tommy1729 [2015] s(exp(d(x))) = x + 2 tommy1729 1 4,228 03/26/2015, 05:35 PM Last Post: tommy1729 Conjecture on semi-exp base change [2015] tommy1729 0 3,344 03/24/2015, 03:14 PM Last Post: tommy1729 [2015] New zeration and matrix log ? tommy1729 1 5,912 03/24/2015, 07:07 AM Last Post: marraco

Users browsing this thread: 1 Guest(s)