We show that $C^r $ generically in the space of $C^r$ conservative diffeomorphisms of a compact surface, every hyperbolic periodic point has a transverse homoclinic orbit.

中文翻译：

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用于保持表面微分同胚的同宿轨道

我们表明$C^r $一般在空间$C^r$紧表面的保守微分同胚，每个双曲周期点都有一个横向同宿轨道。