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Properties of the invariant disk packing in a model bandpass sigma-delta modulator. (English) Zbl 1056.37059
Summary: 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.
##### MSC:
 37E99 Low-dimensional dynamical systems 37J10 Symplectic mappings, fixed points (dynamical systems) 37N99 Applications of dynamical systems 94C05 Analytic circuit theory