Bifurcation rigidity

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 nume rically for one-parameter families of maps, and we offer an analytical expl anation for this phenomenon. We further present numerical evidence of the s ame phenomenon for two-parameter families, and give a mathematical explanat ion like that for the one-parameter case. (C) 1999 Elsevier Science B.V. Al l rights reserved.