The mechanism of the increase of the generalized dimension of a filtered chaotic time series |
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| Authors: | A Chennaoui J Liebler H G Schuster |
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| Institution: | (1) Institut für Theoretische Physik, Universität Frankfurt, D-6000 Frankfurt-Main, Federal Republic of Germany;(2) Institut für Theoretische Physik und Sternwarte, Universität Kiel, D-2300 Kiel 1, Federal Republic of Germany |
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| Abstract: | The determination of the attractor dimension from an experimental time series may be affected by the influence of filters which are incorporated into many measuring processes. While this is expected from the Kaplan-Yorke conjecture, we show that for one-dimensional maps a weak filter can induce a self-similarity which is responsible for the increase of the Hausdorff dimension. We are able to calculate the increase of the generalized dimensionD
q
for the filtered time series of the logistic mapx
i
+1=rx
i
(1–x
i
) atr=4 analytically. |
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| Keywords: | Frobenius-Perron integral equation filtered time series of one-dimensional maps Liapunov exponent Hausdorff dimension generalized dimensionD
q
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