2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143522We show that for a $C^1$ residual subset of diffeomorphisms far away from homoclinic tangency, the stable manifolds of periodic points cover a dense subset of the ambient manifold. This gives a partial proof to a conjecture of C. Bonatti.Dynamical SystemsGeneral Topology37D30;37D05;37D10;37B25;text