2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66898Generically, the set of points along which two non-singular vector fields on the three-sphere are positively (resp. negatively) collinear form a link. We prove that the two vector fields are homotopic if and only if the linking number of those links is zero. We use this criterion to give a new proof of a result of Yano: every non-singular vector field on the three-sphere is homotopic to a non-singular Morse-Smale vector field.16 pages, 6 figuresDynamical SystemsGeometric Topology37D15, 55Q99text