= Averaged amplitude equation
{title2=$\dot r=\epsilon\langle\dot H/\epsilon\rangle/H'(r)$}
An <averaged amplitude equation> describes the slow evolution of a <periodic orbit>'s amplitude under a weak perturbation. If unperturbed energy is $H(r)$ with $H'(r)\ne0$, divide the mean energy drift over one fast period by $H'(r)$. Simple zeros identify attracting or repelling persistent <periodic orbits> according to the derivative of this drift; this approximation is local to an appropriate perturbative amplitude range.
Back to article page
