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.
Original language | English |
---|---|
Article number | 046214 |
Number of pages | 19 |
Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |
Volume | 84 |
Issue number | 4 |
DOIs | |
Publication status | Published - 25 Oct 2011 |
Keywords
- Ginzburg-Landau equation
- Kuramoto-Sivashinsky equation
- inertial manifolds
- characteristic exponents
- dynamical-systems
- attractors
- turbulence
- subspaces
- behavior
- angles