= Real quadratic iteration map
{title2=$x_{n+1}=\mu-x_n^2$}
= Quadratic iteration map
{synonym}
The family $x_{n+1}=\mu-x_n^2$ has <fixed points> $(-1\pm\sqrt{1+4\mu})/2$. Its upper branch attracts linearly for $-1/4<\mu<3/4$ and loses <Lyapunov stability>[stability] in a <period-doubling bifurcation>. The resulting <period-two orbit>[two-cycle] has points $(1\pm\sqrt{4\mu-3})/2$ and <multiplier of a periodic orbit of an iteration>[multiplier] $4(1-\mu)$, <asymptotic stability>[attracting] for $3/4<\mu<5/4$. At $\mu=2$, the <discrete dynamical system>[map] is <topological conjugacy>[conjugate] on $[-2,2]$ to the full <tent map>.
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