Suppose $f:S^2\rightarrow S^2$ is a diffeomorphism. Is true that $f$ must have a fixed point or a point $x\in S^2$ such that $f(f(x))=x$?
Diffeomorphism on the Sphere
4
$\begingroup$
analysis
-
0Not that I see. But I'm sure there are other approaches in the world. I'll leave it there. – 2012-12-12