2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60967In this paper, we use Conley index theory to examine the Poincare index of an isolated invariant set. We obtain some limiting conditions on a critical point of a planar vector field to be an isolated invariant set. As a result we show the existence of infinitely many homoclinic orbits for a critical point with the Poincare index greater than one.Dynamical Systems37B30; 37C29text