Tune domain behavior of single magnet lattices

Single-sextupole and single-octupole lattices ``exhibit .. all the typical properties of more complicated mappings and dynamical issues'', including horizontal resonances of all orders $N$ with island tunes $Q_I$. In general both island tune response spectra and tune modulation drive spectra have multiple lines. Stable motion in transverse phase space is compromised when a pair of drive and response lines align. This vulnerability is illustrated by realistic examples from the Relativistic Heavy Ion Collider.