In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.
A weaker version of the theorem was originally conceived by Henri Poincaré (1892), although he lacked a complete proof which was later given by Ivar Bendixson (1901).
Nevertheless, it is possible to classify the minimal sets of continuous dynamical systems on any two-dimensional compact and connected manifold due to a generalization of Arthur J.
[4][5] One important implication is that a two-dimensional continuous dynamical system cannot give rise to a strange attractor.
If a strange attractor C did exist in such a system, then it could be enclosed in a closed and bounded subset of the phase space.