From Poincaré–Bendixson theorem follows, that second order differential equations of one variable cannot exhibit chaotic behavior. Does anyone know if the theorem holds for a complex differential equation of the type $$ \ddot{z}=f(\dot{z},z), $$ where $z(t)\in \mathbb{C}$ and $f$ is a holomorphic function? Are all such equations non-chaotic?
2026-03-28 17:42:00.1774719720
Can a complex differential equation of the second order exhibit chaotic behavior?
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