05/15/2020, 12:10 PM

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

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