= Ricker population map two-cycle
{c}
{title2=$u_\pm=L\pm d,\quad\tanh(d/2)=d/L$}
For $H(u)=rue^{-u}$ and $L=\log r$, a nonzero second-iterate <fixed point> satisfies $u+H(u)=2L$. A genuine pair has the displayed form, and its <periodic-orbit multiplier> is $(1-L)^2-d^2$. At $r=9$, the pair is exactly $\log3,3\log3$, with <periodic-orbit multiplier> $(1-\log3)(1-3\log3)\simeq0.2264$. For large $r$ its upper point is asymptotic to $2\log r$ and the pair <periodic-orbit multiplier> to $1-2\log r$, so eventual instability follows despite the small <derivative> at the upper point.
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