Let χ be an analytic vector field defined in a real-analytic manifold of dimension three. We prove that all the singularities of χ can be made elementary by a finite number of blowing-ups in the ambient space.
This work has been partially supported by the CNPq/Brasil Grant 205904/2003-5 and Fapesp Grant 02/03769-9.
"Resolution of singularities of real-analytic vector fields in dimension three." Acta Math. 197 (2) 167 - 289, 2006. https://doi.org/10.1007/s11511-006-0011-7