title: Discontinuous and nondifferentiable functions and dimension increase induced by filtering chaotic data.
abstract: We show that one can use recently introduced statistics for continuity and differentiability to show the effect of filters of infinite extent in time on a chaotic time series. The statistics point to a discontinuous or nondifferentiable function between the unfiltered attractor and the filtered attractor as the origin of attractor dimension increase when the filtering is severe. The density of discontinuities as a function of resolution follows a scaling relation. We present direct visualization of this effect in the filtered Henon attractor where the origin of dimension increase becomes obvious.
authors.affiliation: Naval Research Laboratory, Code 6341, Washington, D.C. 20375.
authors.forename: Louis M.
authors.initials: LM
authors.lastname: Pecora
authors.forename: Thomas L.
authors.initials: TL
authors.lastname: Carroll