DISCONTINUOUS AND NONDIFFERENTIABLE FUNCTIONS AND DIMENSION INCREASE INDUCED BY FILTERING CHAOTIC DATA

We show that one can use recently introduced statistics for continuity and differentiability to show the effect of filters of infinite exten t in time on a chaotic time series. The statistics point to a disconti nuous or nondifferentiable function between the unfiltered attractor a nd the filtered attractor as the origin of attractor dimension increas e when the filtering is severe. The density of discontinuities as a fu nction of resolution follows a scaling relation. We present direct vis ualization of this effect in the filtered Henon attractor where the or igin of dimension increase becomes obvious.