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APS » Journals » Phys. Rev. Lett. » Volume 102 » Issue 7
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Phys. Rev. Lett. 102, 074102 (2009) [4 pages]

Hyperbolicity and the Effective Dimension of Spatially Extended Dissipative Systems

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Hong-liu Yang1, Kazumasa A. Takeuchi2,3, Francesco Ginelli2,4, Hugues Chaté2, and Günter Radons1
1Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany
2CEA - Service de Physique de l’État Condensé, CEN Saclay, 91191 Gif-sur-Yvette, France
3Department of Physics, The University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
4Institut des Systèmes Complexes de Paris Ile-de-France, 57-59 Rue Lhomond, 75005 Paris, France

Received 31 July 2008; published 18 February 2009

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.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.102.074102
DOI:
10.1103/PhysRevLett.102.074102
PACS:
05.45.−a, 02.30.Jr, 05.90.+m
 
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