Poincare map trouble

Question

Consider $ X' = F(X)$, $F \in C^1(\mathbb{R}^2)$. Suppose that the system has an orbit $\mathcal{O}_p$ and $\Sigma$ an transversal section in $P$. Show that if $$\pi^{n+1}(\Sigma) \subset \pi^{n}(\Sigma)$$ and $$\bigcap_{n \geq 1}\pi^{n}(\Sigma) = \mathcal{O} $$ then $\mathcal{O}$ is Lyapunov asymptotically stable.