AI 中文总结
该研究证明三维Anosov流在满足稳定与不稳定叶状结构可定向时，其满周期轨道补集为双曲流形，还明确了可定向条件的必要性，并给出悬挂流与测地流的相关结果。
AI 中文摘要
我们证明，若三维流形上的Anosov流具有可定向的稳定和不稳定叶状结构，则任意满周期轨道的补集是双曲流形。这推广了双曲曲面单位切丛中闭满测地线轨道补集的已知情况。此外，我们通过构造无此性质时的反例，证明不变叶状结构的可定向条件是必要的。对于悬挂流，我们得到所有周期轨道集合的补集是双曲的；而对于测地流（无论不变叶状结构是否可定向），所有满且无环的周期轨道集合的补集是双曲的。
英文摘要
We show that if an Anosov flow on a 3-dimensional manifold has orientable stable and unstable foliations, then the complement of any filling periodic orbit is a hyperbolic manifold. This generalizes the known case of the complement of a closed, filling geodesic orbit in the unit tangent bundle of a hyperbolic surface. Furthermore, we show that the orientability condition on invariant foliations is necessary, by constructing a counterexample in the absence of this property. In the case of the suspension flows we obtain that the complement of every collection of periodic orbits is hyperbolic, while for the geodesic flow (regardless of orientability of the invariant foliations) the complement of every filling and anannular collection of periodic orbits is hyperbolic.
Comments26 pages, 5 figures
