= Renormalization of the tent map near its fixed point
{title2=$h\circ F_\mu^2\circ h^{-1}=F_{\mu^2}$}
For $1<\mu\le\sqrt2$, the interval $J=[1/(\mu+1),\mu/(\mu+1)]$ is invariant under the second iterate of the <tent map>. The affine coordinate $h(x)=(\mu/(\mu+1)-x)/((\mu-1)/(\mu+1))$ conjugates that restriction to the tent map with parameter $\mu^2$. Its two linear pieces give the identity directly. This turns the two-iterate horseshoe threshold into a four-iterate threshold and explains why chaotic invariant sets need not have periodic points near the original nonzero fixed point.
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