2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78317The complete invariant for gradient like Morse-Smale dynamical systems (vector fields and diffeomorphisms) on closed 4-manifolds are constructed. It is same as Kirby diagram in a case of polar vector field without fixed points of index 3.Dynamical SystemsGeometric TopologyPrimary 58F09. Secondary 57N13, 58F25text