The theorem of Poincaré-Bendixson states that: For an open set $U \subset \mathbb{R}^{2}$ and a continuously differentiable vector field $F:U \rightarrow \mathbb{R}^2$ and a compact set $K \subset U$, where F has no equilibrium in K, $p \in K$ and $f:\mathbb{R} \rightarrow K$ is the solution of the initial value problem with an initial value of $f(0)=p$ and if $f$ doesn't reach the boundary of K, then there exists an periodic orbit $z$ so that for every $\epsilon>0$ there exists a $t>0$ with $||f(t)-z||<\epsilon$.
Now I have to formulate and prove the version of the theorem for n=1 (so in $\mathbb{R}$).
I really have no idea how to start on this problem. Could you give me a hint?