### Abstract

The Poincaré-Bendixson theorem is a classical result in the study of
(continuous) dynamical systems. Colloquially, it restricts the
possible behaviors of planar dynamical systems: such systems cannot be
chaotic. In practice, it is a useful tool for proving the existence of
(limiting) periodic behavior in planar systems. The theorem is an
interesting and challenging benchmark for formalized mathematics
because proofs in the literature rely on geometric sketches and only
hint at symmetric cases. It also requires a substantial background of
mathematical theories, e.g., the Jordan curve theorem, real analysis,
ordinary differential equations, and limiting (long-term) behavior of
dynamical systems.

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