Properties of the invariant disc packing in a model bandpass sigma-delta modulator
Ashwin, P., Fu, X-C. and Deane, J. H. B. (2003) Properties of the invariant disc packing in a model bandpass sigma-delta modulator International Journal of Bifurcation and Chaos, 13. pp. 631-641.
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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||1 March 2003|
|Uncontrolled Keywords :||Piecewise isometry, discontinuous dynamical system, symbolic coding, disk packing, sigma-delta modulator|
|Additional Information :||Published in International Journal of Bifurcation and Chaos, 13, 631-641. © 2003 World Scientific Publishing. Click here to visit the journal website.|
|Depositing User :||Mr Adam Field|
|Date Deposited :||27 May 2010 14:41|
|Last Modified :||23 Sep 2013 18:33|
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