Let $M \subset R^n$ be open, $f \in C^1 (M, R^n)$, and $\Phi$ be the flow associated to $x' = f(x)$. Show that $\Phi (k, ·) (k ∈ Z)$ is the discrete flow associated to the diffeomorpism $F = \Phi(1, ·)$. Does every diffeomorphism $F$ arise in such a way?
I figured out the first part since it follows directly as $\Phi (k, .) = \Phi^k (1, .)$ but I am still trying in the second part. Any ideas?