Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster II

DY 27.1: Poster

Thursday, March 26, 2009, 16:00–18:00, P1B

Effective degrees of freedom and hyperbolicity of infinite dimensional systems — •Hongliu Yang and Guenter Radons — Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany

Our numerical studies on hyperbolicity of the one dimensional Kuramoto-Sivashinsky equation reveals a natural splitting of its tangent space, an indecomposable manifold spanned by a set of relatively unstable directions and its complement spanned by the remaining purely decaying directions. The strong hyperbolicity of this splitting indicates that dynamics on this indecomposable manifold of active nontrivial degrees of freedom is uniformly separated from the trivial dynamics of being attracted to that manifold for the remaining degrees of freedom. Moreover, the dimension of the isolated manifold shows a stepwise increase with system size, which indicates the existence of a new characteristic length scale for extensive chaos of infinite dimensional systems.

[1] H.L. Yang, K.A. Takeuchi, F. Ginelli, H. Chaté and G. Radons, “Hyperbolicity and the effective dimension of spatially-extended dissipative systems" arXiv:0807.5073.v2.