Hyperbolicity and the effective dimension of spatially extended dissipative systems

Hong-liu Yang, Kazumasa A. Takeuchi, Francesco Ginelli, Hugues Chate, Guenter Radons

Research output: Contribution to journalArticlepeer-review

61 Citations (Scopus)


Using covariant Lyapunov vectors, we reveal a split of the tangent space of standard models of one-dimensional dissipative spatiotemporal chaos: A finite extensive set of N dynamically entangled vectors with frequent common tangencies describes all of the physically relevant dynamics and is hyperbolically separated from possibly infinitely many isolated modes representing trivial, exponentially decaying perturbations. We argue that N can be interpreted as the number of effective degrees of freedom, which has to be taken into account in numerical integration and control issues.

Original languageEnglish
Article number074102
Number of pages4
JournalPhysical Review Letters
Issue number7
Publication statusPublished - 20 Feb 2009


  • Ginzburg-Landau equation
  • chaos
  • exponents


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