= Fast time in a singular perturbation
{title2=$\tau=t/\epsilon$}
For a fast-slow system $\epsilon\dot x=F(x,y)$, $\dot y=G(x,y)$ with $0<\epsilon\ll1$, the rescaled time $\tau=t/\epsilon$ gives $x_\tau=F$, $y_\tau=\epsilon G$. Away from zeros of $F$, an order-one change of $x$ takes order-one fast time but only order-$\epsilon$ original time, while $y$ changes little. Setting $\epsilon=0$ in these rescaled equations freezes $y$ and produces the leading fast subsystem. This limit differs from the slow reduction $F=0$ in the original time; matching the two describes a <relaxation oscillation>.
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