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

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

Please use this identifier to cite or link to this item: http://hdl.handle.net/10036/22376

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Title: Properties of the invariant disk packing in a model bandpass sigma-delta modulator
Author: Ashwin, Peter
Fu, Xin-Chu
Deane, Jonathan
Publisher: 13 (3), pp. 631-641
Journal: International Journal of Bifurcation and Chaos
Date Issued: 2003
URI: http://hdl.handle.net/10036/22376
DOI: 10.1142/S0218127403006753
Links: http://dx.doi.org/10.1142/S0218127403006753
Abstract: In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–Δ 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.
Type: ArticlePreprint
Description: Preprint version of an article published in International Journal of Bifurcation and Chaos, 13, 3, 2003, pp. 631-641. DOI:10.1142/S0218127403006753 © copyright World Scientific Publishing Company. http://www.worldscinet.com/ijbc/ijbc.shtml
Keywords: piecewise isometrydiscontinuous dynamical systemsymbolic codingdisk packingsigma-delta modulator
ISSN: 0218-1274


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