  Global organization of 3-dimensional (3D) Lagrangian chaotic transport is
difficult to infer without extensive computation. For 3D time-periodic flows
with one invariant we show how constraints on deformation that arise from
volume-preservation and periodic lines result in resonant degenerate points
that periodically have zero net deformation. These points organize all
Lagrangian transport in such flows through coordination of lower-order and
higher-order periodic lines and prefigure unique transport structures that
arise after perturbation and breaking of the invariant. Degenerate points of
periodic lines and the extended 3D structures associated with them are easily
identified through the trace of the deformation tensor calculated along
periodic lines. These results reveal the importance of degenerate points in
understanding transport in one-invariant fluid flows.
