论文标题
在某些情况下，Anosov内态的刚性僵硬
Rigidity for Some Cases of Anosov Endomorphisms of Torus
论文作者
论文摘要
在保守的情况下，我们获得了非必要特殊的Anosov内态性质之间的平稳结合。除其他结果外，我们证明了一个非常特殊的$ c^{\ infty} - $ anosov的内态为$ \ mathbb {t}^2 $及其线性化及其线性化，因为它们具有相同的周期性数据。假设对于一个非常特殊的$ c^{\ infty} - $ anosov的$ \ mathbb {t}^2 $每个点的内态是常规的（在Oseledec的定理中），那么我们通过其线性化再次获得了平滑的结合。 我们还获得了$ d $ torus的线性Anosov内态局部刚性的一些结果，其中$ d \ geq 3，在定期数据假设下$。在不变叶上定义的微分方程的研究在刚性问题（例如此处处理的问题）中起着重要作用。
We obtain smooth conjugacy between non-necessarily special Anosov endomorphisms in the conservative case. Among other results, we prove that a strongly special $C^{\infty}-$Anosov endomorphism of $\mathbb{T}^2$ and its linearization are smoothly conjugated since they have the same periodic data. Assuming that for a strongly special $C^{\infty}-$Anosov endomorphism of $\mathbb{T}^2$ every point is regular (in Oseledec's Theorem sense), then we obtain again smooth conjugacy with its linearization. We also obtain some results on local rigidity of linear Anosov endomorphisms of $d-$torus, where $d \geq 3,$ under periodic data assumption. The study of differential equations defined on invariant leaves plays an important role in rigidity problems such as those treated here.
