For a C¹ planar flow, any non-empty compact ω-limit set that contains no fixed points is a periodic orbit. Poincaré 1881, Bendixson 1901. Consequence: planar autonomous systems cannot be chaotic. Applied to Van der Pol, Liénard…
For a C¹ planar flow, any non-empty compact ω-limit set that contains no fixed points is a periodic orbit. Poincaré 1881, Bendixson 1901. Consequence: planar autonomous systems cannot be chaotic. Applied to Van der Pol, Liénard…