This result is from Chicone's book ODE with Applications:
Suppose that p ∈ Rn and the orbit of the flow φt through the point p is forward complete. If the forward orbit of p has compact closure, then ω(p) is nonempty, compact, and connected.
Later, appears this problem: Construct examples to show that the compactness hypothesis of the Proposition is necessary.
I have looked for many examples for several days, but with no success. I need one example. I will appreciate your help. It is quite urgent. Thanks.