Nearly Hamiltonian system
= Nearly Hamiltonian system
{title2=$\dot z=J\nabla H(z)+\epsilon R(z)$}
A <nearly Hamiltonian system> is a weak perturbation of a <Hamiltonian system>. Along its paths, $\dot H=\epsilon\nabla H\cdot R$. Averaging this drift over an unperturbed <periodic orbit> is the <energy balance method>; a simple zero of the averaged drift selects a persistent nearby <periodic orbit> for sufficiently small $\epsilon$. A multiple zero requires higher-order analysis.