  We discuss the main mechanisms generating chaotic behavior of the quantum
trajectories in the de Broglie - Bohm picture of quantum mechanics, in systems
of two and three degrees of freedom. In the 2D case, chaos is generated via
multiple scatterings of the trajectories with one or more `nodal point -
X-point complexes'. In the 3D case, these complexes form foliations along
`nodal lines' accompanied by `X-lines'. We also identify cases of integrable or
partially integrable quantum trajectories. The role of chaos is important in
interpreting the dynamical origin of the `quantum relaxation' effect, i.e. the
dynamical emergence of Born's rule for the quantum probabilities, which has
been proposed as an extension of the Bohmian picture of quantum mechanics. In
particular, the local scaling laws characterizing the chaotic scattering
phenomena near X-points, or X-lines, are related to the global rate at which
the quantum relaxation is observed to proceed. Also, the degree of chaos
determines the rate at which nearly-coherent initial wavepacket states lose
their spatial coherence in the course of time.
