Let $M$ denotes the Möbius strip. Then is it true that



> 
> For every continuous map $f:M\to M$ there is $x\in M^\circ$ ($x\notin\partial M$) such that $f(f(x))=x$?
> 
> 
> 



A question on continuous maps from Möbius to itself
I might be missing something, but for $f = g\circ h,$ where $h$ is the retraction onto the core circle (see [this question](https://math.stackexchange.com/questions/1241015/show-that-the-m%C3%B6bius-band-has-its-central-circle-c-as-a-deformation-retract)), and $g$ is the rotation of the circle by, say, 1 radian there appears to be no such $x.$


