2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223149In a dynamical system the singular vector (SV) indicates which perturbation will exhibit maximal growth after a time interval $τ$. We show that in systems with spatiotemporal chaos the SV exponentially localizes in space. Under a suitable transformation, the SV can be described in terms of the Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us to deduce a universal power law $τ^{-γ}$ for the localization of the SV. Moreover the same exponent $γ$ characterizes the finite-$τ$ deviation of the Lyapunov exponent in excellent agreement with simulations. Our results may help improving existing forecasting techniques.5 pagesChaotic DynamicsStatistical Mechanicstext