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.
|Number of pages||19|
|Journal||Physical Review. E, Statistical, Nonlinear and Soft Matter Physics|
|Publication status||Published - 25 Oct 2011|
- Ginzburg-Landau equation
- Kuramoto-Sivashinsky equation
- inertial manifolds
- characteristic exponents