= Feigenbaum constants
{c}
{title2=$\alpha,\delta$}
{wiki}
For a generic quadratic <period-doubling cascade>, the Feigenbaum constants are the limiting parameter ratio $\delta$ and spatial ratio $\alpha$. With $s_n$ the successive superstable period-$2^n$ parameters and $d_n=f_{s_n}^{2^{n-1}}(0)$ the signed central-orbit spacing,
$$
\delta=\lim_{n\to\infty}\frac{s_n-s_{n-1}}{s_{n+1}-s_n},\qquad
\alpha=-\lim_{n\to\infty}\frac{d_n}{d_{n+1}}.
$$
The positive convention gives $\delta\simeq4.669201609$ and $\alpha\simeq2.502907875$. The orientation-reversing spatial scale at the <Feigenbaum renormalization fixed point> is $a=-1/\alpha$.
// Target: dynamical-systems.bigb
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