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Brian R. Hunt, Jason A. C. Gallas, Celso Grebogi, James A. Yorke, and
Huseyin Kocak

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Physica D 129 (1999), 35-56.
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Online abstract and download information

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.

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*Updated: June 17, 1999*