Bifurcation Rigidity

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

Physica D 129 (1999), 35-56.

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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.

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