On the Fractal Dimension of Filtered Chaotic Signals
Much progress has been done in the reconstruction of the geometry of strange attractors, from experimental single time-series, exploiting embedding techniques [l], which make possible, for instance, the estimation of fractal dimensions and metric entropies. A particularly relevant aspect of these procedures, which has not yet been pointed out, concerns the role of filtering. In fact, not only any measurement of experimental signals is to some extent filtered, due to the finite instrumental bandwidth, but often an explicit intervention of the observer is present as well, motivated by the need of “cleaning” the system’s output from the presence of noise.
KeywordsEntropy Manifold Lution Reso Bedding
Unable to display preview. Download preview PDF.
- 1.F. Takens, in Lecture Notes in Mathematics 898, D.A. Rand and L.S. Young eds. (Springer, Berlin 1981)Google Scholar
- 2.J.L. Kaplan and J.A. Yorke, in Lecture Notes in Mathematics 730, H.O. Peitgen and H.O. Walther eds. (Springer, Berlin 1979)Google Scholar
- 3.Y. Aizawa, this volumeGoogle Scholar