Sensitive Parameter Dependence Of Autocorrelation Function In Piecewise Linear Maps

This paper is principally concerned with the effect of splitting and permuting, or shifting, the branches of an onto piecewise linear map, with particular regard to the effect on the autocorrelation of the associated chaotic sequence. This is shown to be a chaotic function of the shifting parameter of the map, and its sensitivity with respect to minute changes in this parameter is termed autocorrelation chaos. This paper presents both analytical and computational studies of the phenomenon.