Hyperbolicity and the effective dimension of spatially-extended dissipative systems

Details Hyperbolicity and the effective dimension of spatially-extended dissipative systems Hyperbolicity and the effective dimension of spatially-extended dissipative systems

2008-07-31

arxiv.org/abs/0807.5073v2

Phys. Rev. Lett. 102, 074102 (2009)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.102.074102

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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