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Fractal dimension of transport coefficients in a deterministic dynamical system | | Zbigniew Koza
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4 May 2004 | | Subject: | Chaotic Dynamics | nlin.CD | | Abstract: | In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters. | | Source: | arXiv, nlin.CD/0405006 | | Services: | Forum | Review | PDF | Favorites | |
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