Properties of the invariant disc packing in a model bandpass sigma-delta modulator

In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Sigma–Delta modulator. The periodically coded regions form a packing of the forward invariant phase space by invariant disks. For this one-parameter family of PWIs, by introducing codings underlying the map operations we give explicit expressions for the centers of the disks by analytic functions of the parameters, and then show that tangencies between disks in the packings are very rare; more precisely they occur on parameter values that are at most countably infinite. We indicate how similar results can be obtained for other plane maps that are piecewise isometries.