= Mitchell Feigenbaum
{c}
{wiki}
<Mitchell Feigenbaum> discovered quantitative universality in period-doubling sequences of nonlinear maps. For a class of smooth maps with a quadratic maximum, successive parameter intervals shrink with a limiting ratio near $4.669$, one of the <Feigenbaum constants>.<Quantitative Universality for a Class of Nonlinear Transformations by Mitchell Feigenbaum>[Universal scaling analysis for maps with a specified maximum exponent]{ref}
The striking result is independence from many details of the map, within the stated universality class. The <Feigenbaum renormalization fixed point> expresses that repeated rescaling approaches one common structure. A different shape of the critical maximum can belong to a different class, so the numerical constant is not universal for every nonlinear system.
Back to article page
