Trajectories approaching an unstable equilibrium point

Question

Let $V$ be a $C^k$ vector field in $\mathbb{R}^n$, $x \in \mathbb{R}^n$ be an equilibrium point of $V$, and $J = DV(x)$ be the corresponding Jacobian matrix. Assume that $J$ has an eigenvalue with positive real part. Can exist an open set $U$ such that all trajectories assotiated to $V$ starting in $U$ converges to $x$ when the time goes to infinity?