2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59452We develop the idea of self-indexing and the technology of gradient-like vector fields in the setting of Morse theory on a complex algebraic stratification. Our main result is the local existence, near a Morse critical point, of gradient-like vector fields satisfying certain ``stratified dimension bounds up to fuzz'' for the ascending and descending sets. As a global consequence of this, we derive the existence of self-indexing Morse functions.19 pages, AMS-LaTeX, replaced with revised versionAlgebraic GeometryDynamical Systems14J17; 32S60; 37D15text