  We introduce a map which reproduces qualitatively many fundamental properties
of the dynamics of heavy particles in fluid flows. These include a uniform rate
of decrease of volume in phase space, a slow-manifold effective dynamics when
the single parameter $s$ (analogous of the Stokes number) approaches zero, the
possibility of fold caustics in the "velocity field", and a minimum, as a
function of $s$, of the Lyapunov (Kaplan-Yorke) dimension of the attractor
where particles accumulate.
