I am not quite sure if everything I will post here is completely true, but I have a question about chaotic attractors in two-dimensional systems.
I believe the Poincare-Bendixson theorem implies that chaotic attractors only occur in systems of dimension three or higher.
Van der Pol oscillator - Scholarpedia
it states that the Van der Pol oscillator (which I think is a two-dimensional system) exerts chaos and has a chaotic attractor. Wouldn't that contradict the above theorem though?
The same thing is said for the Duffing oscillator
Duffing oscillator - Scholarpedia
Clearly I know these systems don't disprove the above theorem (it can't be that simple), so how is it that they exert chaos?