2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221051We show, using covariant Lyapunov vectors, that the chaotic solutions of spatially extended dissipative systems evolve within a manifold spanned by a finite number of physical modes hyperbolically isolated from a set of residual degrees of freedom, themselves individually isolated from each other. In the context of dissipative partial differential equations, our results imply that a faithful numerical integration needs to incorporate at least all physical modes and that increasing the resolution merely increases the number of isolated modes.4 pages, 4 figuresChaotic DynamicsStatistical Mechanicstext