本文研究闭 3-流形上测地流有限覆盖的 Anosov 流分类，证明当覆盖指数 n 为奇数时只有一个轨道等价类，n 为偶数时恰有两个轨道等价类。
摘要：
设 $M$ 是一个闭 3-流形，它沿纤维在闭曲面的单位切丛上允许一个指数为 n 的有限覆盖。我们证明：若 n 为奇数，则 M 上在轨道等价意义下只有一个 Anosov 流；若 n 为偶数，则 M 上存在两个 Anosov 流的轨道等价类。
英文摘要：
Let $M$ be a closed 3-manifold admitting a finite cover of index n along the fibers over the unit tangent bundle of a closed surface. We prove that if n is odd, there is only one Anosov flow on M up to orbital equivalence, and if n is even, there are two orbital equivalence classes of Anosov flows on M.
We demonstrate that the question whether or not a given postcritically finite topological ramified covering map of the 2-sphere is Thurston equivalent to a rational map is algorithmically decidable.
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