  We study the dynamics of resonances of analytic perturbations of 0th order
pseudodifferential operators $P(s)$. In particular, we prove a Fermi golden
rule for resonances of $P(s)$ at embedded eigenvalues of $P=P(0)$. We also
study the dynamics of eigenvalues of $P(t)=P+it\Delta$ as the eigenvalues
converge to simple eigenvalues of $P$. The 0th order pseudodifferential
operators we consider satisfy natural dynamical assumptions and are used as
microlocal models of internal waves.
