We discuss the kinematics of three-dimensional, time-dependent and time-independent fluid flows in geometrical and statistical terms. Two types of flows arise as typical: those that can be reduced to action-action-angle maps and action-angle-angle maps. A study of transport and mixing in these two types of flows will be presented: existence and non-existence of invariant objects, statistical quantities such as dispersion, and the relationship between the two. Similarities and differences with the behavior of two-dimensional, time dependent flows will be emphasized.

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