 Periodic analytic iterations by Riemann mapping - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Periodic analytic iterations by Riemann mapping (/showthread.php?tid=1068) Periodic analytic iterations by Riemann mapping - tommy1729 - 03/02/2016 Let r denote riemann mapping. r' denotes the functional inverse of r. Let j be An analytic jordan curve around the origin. R maps j to the unit circle. Let r'(1) be the starting point A. then iterations f^[x](r'(1)) with x > 0 ( real ) are periodic and analytic iff F(z) = r' ( T ( r) ). Where T is a complex number on the unit circle. I think this is correct. This seems to suggest exp has no periodIC iterational Jordan curve away from its fixpoints. Regards Tommy1729 RE: Periodic analytic iterations by Riemann mapping - tommy1729 - 03/05/2016 Strongly related http://math.eretrandre.org/tetrationforum/showthread.php?tid=1038 Regards Tommy1729