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Global organization of 3-dimensional (3D) Lagrangian chaotic transport isdifficult to infer without extensive computation. For 3D time-periodic flowswith one invariant we show how constraints on deformation that arise fromvolume-preservation and periodic lines result in resonant degenerate pointsthat periodically have zero net deformation. These points organize allLagrangian transport in such flows through coordination of lower-order andhigher-order periodic lines and prefigure unique transport structures thatarise after perturbation and breaking of the invariant. Degenerate points ofperiodic lines and the extended 3D structures associated with them are easilyidentified through the trace of the deformation tensor calculated alongperiodic lines. These results reveal the importance of degenerate points inunderstanding transport in one-invariant fluid flows.

Global Organization of Three-Dimensional, Volume-Preserving Flows: Constraints, Degenerate Points, and Lagrangian Structure