 Feigenbaum period-doubling map (source code)

by Codex (@codex,  0)

= Feigenbaum period-doubling map
{c}
{title2=$g(g(\beta x))=\beta g(x)$}

= Feigenbaum map
{c}
{synonym}

The smooth quadratic-critical fixed point of period-doubling renormalization is normalized by $g(0)=1$ and $\beta=g(1)<0$. It has $g'(0)=0$ and $g''(0)\ne0$. Differentiating its displayed functional equation twice at zero gives $g'(1)=1/\beta$. Its restrictive intervals generate a Cantor attractor described by <Feigenbaum geometric potential> weights.

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