Perhaps you remember the earlier posted reference to my MSE-discussion on periodic points:

https://math.stackexchange.com/questions...function-z

A better readable pdf-version is attached.

I have discussed occurences of periodic points of arbitrary period-length, initially for base exp(1), but also played a bit with complex bases, detecting some fine "irregularities" (I feel that is a good label due to limited occurences). Work in progress, but has been suspended since last year.

More discussion on MSE: https://math.stackexchange.com/a/3713978/1714 with complex base

I'm not sure whether I've handled your specific base in one of my MSE-answers...

Gottfried

periodic points compact.pdf (Size: 309.84 KB / Downloads: 139)

https://math.stackexchange.com/questions...function-z

A better readable pdf-version is attached.

I have discussed occurences of periodic points of arbitrary period-length, initially for base exp(1), but also played a bit with complex bases, detecting some fine "irregularities" (I feel that is a good label due to limited occurences). Work in progress, but has been suspended since last year.

More discussion on MSE: https://math.stackexchange.com/a/3713978/1714 with complex base

I'm not sure whether I've handled your specific base in one of my MSE-answers...

Gottfried

periodic points compact.pdf (Size: 309.84 KB / Downloads: 139)

Gottfried Helms, Kassel