Global organization of three-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.

中文翻译：

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三维，保体积流的全局组织：约束，退化点和拉格朗日结构

如果不进行大量计算，则很难推断出三维（3D）拉格朗日混沌传输的全局组织。对于具有一个不变性的3D时间周期流，我们显示了体积守恒和周期线引起的变形约束如何导致谐振退化点周期性地具有零净变形。这些点通过协调低阶和高阶周期线来组织所有拉格朗日输运，并预示了在扰动和破坏不变式之后产生的独特输运结构。通过沿着周期线计算出的变形张量的轨迹，可以轻松地识别周期线的退化点以及与之关联的扩展3D结构。