# Tetration Forum

Full Version: [MSE] Fixed point and fractional iteration of a map
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I've asked this question few days ago on MSE, is about the behaviour of the fractional iterates when there are fixed points. I know that in this forum there was alot of works on the fixed point and stuff, by I have to admit that I can't understand alot.
The better strategy here would be to study some literature and start from 0, anyways at the moment I don't really have alot of time so I started with a very specific question.

http://math.stackexchange.com/questions/...nk-is-anot

The question is the following:

1 - If $k$ is a fixed point of the map $F:X\rightarrow X$ and ..

2 - exist a map $\Psi:X\rightarrow X$ such that $\Psi^{\circ n}=F$ (aka $\Psi$ behaves as a $1\over n$-iterate of $F$ )

prove that $\Psi(k)$ is also a fixed point of $F$

On MSE I give a proof but I'm not sure if it is formal, if somone want to try there is a 100 reps bounty there.

PS: If my proof is correct then I guess that even $\Psi(\Psi(k))$, $\Psi^{\circ 3}(k)$, $\Psi^{\circ 4}(k)$ .... exc.. are all fixed points of $F$