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 , one of the Feigenbaum constants.[ref]
Quantitative Universality for a Class of Nonlinear Transformations by Mitchell Feigenbaum. Universal scaling analysis for maps with a specified maximum exponent
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.
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Mitchell Feigenbaum is an American mathematical physicist renowned for his groundbreaking work in the field of chaos theory. He is best known for discovering the Feigenbaum constants, which describe the geometrical properties of bifurcations in dynamical systems. Specifically, these constants characterize how systems transition from orderly and periodic behavior to chaotic behavior through a process known as period-doubling bifurcation.