Is there any nonempty, compact and invariant set in dynamical system generated by this system of equations?
My idea is to use this fact: Not empty omega limit set - because here we have also bounded functions and omega limit set is invariant. But it's hard to say anything about compactness.
Thanks a lot for your help.
Edit: Of course is not true that omega limit set is always invariant - it is only when it lays in trajectory. That makes problem harder and probably it's not a good way.