= Hyperbolic characteristic flow for an inverted oscillator
{title2=$A_t=\begin{pmatrix}\cosh t&\sinh t\\\sinh t&\cosh t\end{pmatrix}$}
The <Hamiltonian> $(v^2-x^2)/2$ gives $\dot x=v$, $\dot v=x$. Its <characteristic flow map> is multiplication by $A_t$, with $A_tA_s=A_{t+s}$ and determinant one. The backward map is $A_{-t}$. This expanding-contracting linear flow preserves phase-space <Lebesgue measure> and every finite-$p$ <integral> of a transported density, despite stretching its level sets.
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