2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125836Let X be an analytic vector field defined in a real analytic manifold of dimension three. We prove that all the singularities of X can be made elementary by a finite number of blowing-ups in the ambient space. New version: Some misprints have been corrected and the text have been slightly reorganized. The final version appears in Acta Mathematica -Volume 197, Number 2, 167-289.100 pages, 28 figuresAlgebraic GeometryClassical Analysis and ODEs14E15; 34C05; 58F14text