Timeline for How to solve $f(f(x)) = \cos(x)$?
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| Nov 2, 2016 at 23:00 | comment | added | user78249 | @WillJagy I've devoured everything there already unfortunately. I actually have my own formula for the half iterate of $\sin$ on the real line. By taking the uniform convergence of $f_n(x) = (1-1/n)\sin(x)$ to $\sin(x)$ on $\mathbb{R}$ one can show $f_n^{\circ t}(x) \to f^{\circ t}(x)$ given the above representation with $t \in \mathbb{R}^+$. It produces the exact graph you posted too. I was unable to show analycity though, only continuity. | |
| Nov 2, 2016 at 22:31 | comment | added | Will Jagy | see mathoverflow.net/questions/45608/… and my self-answer I'm afraid the web page with those references is down but I have pdfs at home for the shorter pieces. Especially recommend I. Noel Baker | |
| Oct 18, 2016 at 19:36 | history | answered | user78249 | CC BY-SA 3.0 |