Journal of Statistical Physics, Vol. 59, Nos. 5/6, 1990, p. 1311-1328.
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 dimension D_q for the filtered time series of the logistic map x_(i+1)= rx_i(1- x_i) at r = 4 analytically.