From where can I study more examples on non-wandering set? @AnthonyQuas

The flow is defined by $$\phi_{t}(x) : \mathbb{R} \to \mathbb{R}$$ For $\dot{x} = 0$, we have $$\phi_{t}(x) = x$$ For this case: $$\phi_{t}(\mathbb{R}) \ \cap \ \mathbb{R} \neq \emptyset$$ and hence I can conclude that the entire real line(which is connected) is a non-wandering set. Is that right?@AnthonyQuas

Thank you for your answer. Can you be more specific by explicitly writing the non-wandering sets for both the examples?