KnowraPoincaré–Bendixson theoremLinked fromLinked fromThe 4 pages that link to Poincaré–Bendixson theorem, each with the reason it gives.All 4Broader topic 1Related 1Compared with 2Henri PoincaréBroader topic: It exemplifies his approach of classifying limiting behavior without solving trajectories explicitly.Periodic orbitRelated: It gives conditions under which planar trajectories must approach a periodic orbit.Bendixson–Dulac theoremCompared with: It can support cycle-existence arguments, while Bendixson–Dulac supplies a cycle-exclusion test.Sharkovsky's theoremCompared with: It is another low-dimensional restriction on dynamics, but concerns continuous-time planar flows.