Poincaré–Bendixson theorem

Question

Does someone know a good reference for a proof of the Poincaré–Bendixson theorem using the language of vector fields?

Answer 1

If you read French you can look at this one, which is really nice :

Serge Cantat, Théorème de Poincaré-Bendixson, Le journal de maths des élèves, ENS Lyon, vol. 1, no 3,‎ 1995; http://math.univ-lyon1.fr/~benzoni/CantatJME3.pdf (Wayback Machine)

Answer 2

Look at Hirsch-Smale (or, I presume, Hirsch-Smale-Devaney) Differential Equations, Dynamical Systems, ...