Lm. Pecora et Tl. Carroll, DISCONTINUOUS AND NONDIFFERENTIABLE FUNCTIONS AND DIMENSION INCREASE INDUCED BY FILTERING CHAOTIC DATA, Chaos, 6(3), 1996, pp. 432-439
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.