ON LOCAL AND GLOBAL RIGIDITY OF QUASI-CONFORMAL ANOSOV DIFFEOMORPHISMS
ON LOCAL AND GLOBAL RIGIDITY OF QUASI-CONFORMAL ANOSOV DIFFEOMORPHISMS
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拟共角阿诺索夫微分态的局部和全局刚性
DOI：
10.1017/s1474748003000161
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发表时间：
2003
影响因子：
0.9
通讯作者：
V. Sadovskaya
中科院分区：
文献类型：
--
作者：
B. Kalinin;V. Sadovskaya
考虑紧流形$\mathcal{M}$的传递一致拟共形Anosov微分同胚$f$。我们证明了如果稳定分布和不稳定分布的维数大于2，那么$f$是$C^\infty$共轭于环面有限因子的仿射Anosov自同构。如果维度至少是两个，那么在$\mathcal{M}$是一个基础流形的附加假设下，同样的结论成立。并给出了微分同胚与小扰动之间共轭光滑的充分必要条件。AMS 2000数学学科分类：初级37C；37d
We consider a transitive uniformly quasi-conformal Anosov diffeomorphism $f$ of a compact manifold $\mathcal{M}$. We prove that if the stable and unstable distributions have dimensions greater than two, then $f$ is $C^\infty$ conjugate to an affine Anosov automorphism of a finite factor of a torus. If the dimensions are at least two, the same conclusion holds under the additional assumption that $\mathcal{M}$ is an infranilmanifold. We also describe necessary and sufficient conditions for smoothness of conjugacy between such a diffeomorphism and a small perturbation. AMS 2000 Mathematics subject classification: Primary 37C; 37D