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arXiv · 0807.5073

Hyperbolicity and the effective dimension of spatially-extended dissipative systems

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

We show, using covariant Lyapunov vectors, that the chaotic solutions of spatially extended dissipative systems evolve within a manifold spanned by a finite number of physical modes hyperbolically isolated from a set of residual degrees of freedom, themselves individually isolated from each other. In the context of dissipative partial differential equations, our results imply that a faithful numerical integration needs to incorporate at least all physical modes and that increasing the resolution merely increases the number of isolated modes.

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Hong-liu Yang, Kazumasa A. Takeuchi, Francesco Ginelli, Hugues Chaté, Günter Radons. 2008-10-24. Hyperbolicity and the effective dimension of spatially-extended dissipative systems. https://doi.org/10.1103/physrevlett.102.074102

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