Geometric intuition of bounded trajectory and connectedness

Question

Property of Omega-limit set:

Let x be a point on a manifold and $\Psi_{t}\left ( x \right )$ be a trajectory through x. If $\Psi_{t}\left ( x \right )$ is bounded, then the omega limit set $L_{\omega}$ is connected.

Could anyone be kind enough to provide a simple illustration for me to wrap my head around this?

Thanks in advance.