= Feigenbaum renormalization fixed point
{c}
{title2=$g=\mathcal T(g)$}
= Feigenbaum fixed point
{c}
{synonym}
A Feigenbaum <fixed point> is an even analytic <unimodal interval map> $g$ with $g(0)=1$, a critical maximum of even order $d$, $a=g(1)\in(-1,0)$ and
$$
g(x)=a^{-1}g(g(ax)).
$$
In the quadratic class $g''(0)<0$. Its spatial scaling uses the <Feigenbaum constants> convention $\alpha=-1/a$; the values depend on the critical order. The central restrictive intervals are successively reduced by $|a|$ under renormalization. This <fixed point> describes the limiting shape of repeatedly renormalized maps at a period-doubling accumulation.
// Target: dynamical-systems.bigb
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