The Poincaré-Bendixson Theorem is a fundamental result in the study of dynamical systems, particularly for two-dimensional flows, which states that for a compact, non-empty limit set that does not contain equilibria, the limit set must consist of a periodic orbit or a fixed point. This theorem connects the behavior of trajectories in phase portraits to the existence of limit cycles and provides insights into the long-term behavior of nonlinear differential equations.
congrats on reading the definition of Poincaré-Bendixson Theorem. now let's actually learn it.