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arXiv · 1107.2567

Hyperbolic decoupling of tangent space and effective dimension of dissipative systems

Kazumasa A. Takeuchi·Hong-liu Yang·Francesco Ginelli·Günter Radons·Hugues Chaté
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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.

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Kazumasa A. Takeuchi, Hong-liu Yang, Francesco Ginelli, Günter Radons, Hugues Chaté. 2011-07-13. Hyperbolic decoupling of tangent space and effective dimension of dissipative systems. https://doi.org/10.1103/physreve.84.046214

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