AI 中文总结
本文构造了一类与环面双曲自同态同伦但不与任何Anosov局部微分同胚半共轭的局部微分同胚，并证明二维环面上具有扩张方向的非可逆部分双曲$C^1$局部微分同胚若半共轭于Anosov局部微分同胚，则其自身必为Anosov。
AI 中文摘要
我们给出了一类与环面双曲自同态同伦的局部微分同胚，但在恒等映射的同伦类中，它们不与任何Anosov局部微分同胚拓扑半共轭。特别地，我们证明对于二维环面上具有扩张方向的非可逆部分双曲$C^1$光滑局部微分同胚，若它与某个Anosov局部微分同胚半共轭，则它本身也是Anosov局部微分同胚。
英文摘要
We give a class of local diffeomorphisms which are homotopic to toral hyperbolic endomorphisms, but which are not topologically semi-conjugate, within the homotopic class of the identity, to any Anosov local diffeomorphism. In particular, we show that for a non-invertible partially hyperbolic $C^1$-smooth local diffeomorphism with expanding directions on the $2$-torus, if it is semi-conjugate to an Anosov local diffeomorphism, then it is also an Anosov local diffeomorphism.
Comments21 pages, 1 figure. Comments are welcome!
