We show that if a closed smooth n-manifold M admits a u-dimension one special Anosov endomorphism f, then M is homeomorphic to ${\mathbb{T}}^n$ and f is topologically conjugate to a hyperbolic toral endomorphism. Moreover, any u-dimension one special Anosov endomorphism is transitive and the stable foliation is minimal.

中文翻译：

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关于余维一特殊Anosov自同态

我们证明，如果一个封闭光滑的n -流形M允许一个u维一特殊 Anosov 自同态f，则M同胚于${\mathbb{吨}}^n$并且f在拓扑上与双曲托拉自同态共轭。此外，任何u维一特殊 Anosov 自同态是传递的，稳定的叶状结构是最小的。