2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126297The systems of complex analytic second order ordinary differential equations whose solutions close up to become rational curves (after analytic continuation) are characterized by the vanishing of an explicit differential invariant, and turn out to provide an infinite dimensional family of integrable systems.29 pages, 1 figure, v.2 more citations, v.3 more examples, v.4 minor corrections, v.5 minor correctionsDifferential GeometryClassical Analysis and ODEs53A55text