= Quadratic-map conjugacy to the full tent map
{title2=$f(H(u))=H(T(u))$}
The <homeomorphism> $H(u)=-2\cos(\pi u)$ maps $[0,1]$ to $[-2,2]$ and satisfies $H\circ T=f\circ H$, where $T$ is the full <tent map> and $f(x)=2-x^2$. This transfers <dense periodic points>, <topological mixing> and <sensitive dependence on initial conditions>[sensitivity] to the <real quadratic iteration map>[quadratic interval map]. The related circle <discrete dynamical system>[map] $h(y)=-2\cos(2\pi y)$ only gives a <semiconjugacy of dynamical systems>[semiconjugacy] from doubling, because $h(y)=h(1-y)$ and is not <injection>[injective].
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