feigenbaum function

Input interpretation

Feigenbaum function

Alternate name

Feigenbaum-Cvitanović functional equation

Definition

Consider an arbitrary one-dimensional map x_(n + 1) = F(x_n) (with implicit parameter r) at the onset of chaos. After a suitable rescaling, the Feigenbaum function g(x) = lim_(n->∞) 1/(F^(2^n)(0)) F^(2^n)(x F^(2^n)(0)) is obtained. This function satisfies g(g(x)) = - 1/α g(α x), with α = 2.5029....
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Related terms

bifurcation | chaos | Feigenbaum constant

Subject classifications

MathWorld

chaos

MSC 2010

37-XX
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