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Bifurcation diagrams of periodic windows of scalar maps are often found to be not only topologically equivalent, but in fact to be related by a nearly linear change of parameter coordinates. This effect has been observed numerically for one-parameter families of maps, and we offer an analytical explanation for this phenomenon. We further present numerical evidence of the same phenomenon for two-parameter families, and give a mathematical explanation like that for the one-parameter case.Click here for a PostScript copy (450K) of the text of this paper. Tables and figures are available seperately:
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