Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2011-07-13
Nonlinear Sciences
Chaotic Dynamics
21 pages, 30 figures
Scientific paper
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.
Chate' Hugues
Ginelli Francesco
Radons Günter
Takeuchi Kazumasa A.
Yang Hong-liu
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