Hyperbolicity and the effective dimension of spatially-extended dissipative systems
arXiv:0807.5073 · doi:10.1103/PhysRevLett.102.074102
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.
4 pages, 4 figures
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Cited by in corpus (38)
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