  Angle-action maps that are periodic in the action direction can have
accelerator modes: orbits that are periodic when projected onto the torus, but
that lift to unbounded orbits in an action variable. In this paper we construct
a volume-preserving family of maps, with two angles and one action, that have
accelerator modes created at Hopf-one (or saddle-center-Hopf) bifurcations.
Near such a bifurcation we show that there is often a bubble of invariant tori.
Computations of chaotic orbits near such a bubble show that the trapping times
have an algebraic decay similar to that seen around stability islands in
area-preserving maps. As in the 2D case, this gives rise to anomalous diffusive
properties of the action in our 3D map.
