2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113417We numerically study the interplay between heterogeneous dynamics and properties of negatively curved regions of the potential energy surface in a model glassy system. We find that the unstable modes of saddles and quasi-saddles undergo a localization transition close to the Mode-Coupling critical temperature. We also find evidence of a positive spatial correlation between clusters of particles having large displacements in the unstable modes and dynamical heterogeneities.7 pages, 3 figures, submitted to Europhys. LettStatistical MechanicsSoft Condensed Mattertext