title: Hyperbolic decoupling of tangent space and effective dimension of dissipative systems.
abstract: We show, using covariant Lyapunov vectors, that the tangent space of spatially extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled "physical" modes, which carry the physically relevant information of the trajectory, and a residual set of strongly decaying "spurious" modes. The decoupling of the physical and spurious subspaces is defined by the absence of tangencies between them and found to take place generally; we find evidence in partial differential equations in one and two spatial dimensions and even in lattices of coupled maps or oscillators. We conjecture that the physical modes may constitute a local linear description of the inertial manifold at any point in the global attractor.
authors.affiliation: Service de Physique de l'État Condensé, CEA-Saclay, F-91191 Gif-sur-Yvette, France.
authors.forename: Kazumasa A
authors.initials: KA
authors.lastname: Takeuchi
authors.forename: Hong-liu
authors.initials: HL
authors.lastname: Yang
authors.forename: Francesco
authors.initials: F
authors.lastname: Ginelli
authors.forename: Günter
authors.initials: G
authors.lastname: Radons
authors.forename: Hugues
authors.initials: H
authors.lastname: Chaté