ABSTRACT In this note we give a statistical approximation of the unstable manifold of a connected isolated unstable attractor of a smooth flow using coherent measures relative to it. In the main result we show that almost all orbits in the support of a coherent measure relative to an isolated unstable attractor are contained in its unstable manifold.

中文翻译：

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孤立不稳定吸引子的相干测度和不稳定流形

摘要 在本笔记中，我们使用与其相关的相干度量给出了平滑流的连接孤立不稳定吸引子的不稳定流形的统计近似。在主要结果中，我们表明几乎所有支持相对于孤立不稳定吸引子的相干测度的轨道都包含在其不稳定流形中。