On n-periodic points of the exp() - A discussion with pictures and methods - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Computation (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=8) +--- Thread: On n-periodic points of the exp() - A discussion with pictures and methods (/showthread.php?tid=1264) On n-periodic points of the exp() - A discussion with pictures and methods - Gottfried - 05/15/2020 On n-periodic points of the exp() - A discussion with pictures and methods                           Initially triggered by a completely unrelated (seemingly on a first glance) other question in MSE I worked on the problem of periodic points of the exponential function and got a -I think: marvelous- result which I like to share here: MSE - on periodic points of the exp()-function Perhaps I'll transfer the full copy of the text and the images here later, but for the moment I'm bit lazy after that intense researching, computing & documenting. update: another question which asks for generalization to arbitrary (real) bases and their 2-periodic points see  MSE - on 2-periodic points for iterated b^z    (Because this discussion has evolved much and is much worthful, I post another statement pointing at it) update2: a short exposé of my idea in mathoverflow.net and the relevant question: "is my method for finding n-periodic points of exhaustive?" update3 (7'20): A compilation into a draft article see here [attachment=1412]   Gottfried RE: A discussion with pictures of the set of fixed- and n-priodic points of the exp() - Gottfried - 06/10/2020 A very nice discussion I've been involved, but which is now too long to be copied here, is Jun,20 in Math Stack Exchange .      "how to compute the 2-periodic points of $w=z^{z^w}$  .  I apply my newly found method to the example bases   $z$ with protocols of errors and progresses in the iteration and method of finding. This has also developed into a (re-) discussion on Yiannis' generalization of the Lambert-W function, called "HyperW" of "HW()" which he has presented in his article in 2005 (available here in tetration-forum-library Galidakis2005).     See Dominic, Yiannis Galidakis and me in discussion... Gottfried