论文标题
对于圆环上部分双曲动作的某些等轴测扩展的刚度属性
Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus
论文作者
论文摘要
本文研究了某些等距的圆环扩展，以部分双曲线$ \ mathbb {z}^k $（$ k \ geqslant 2 $）的动作。我们证明，如果操作的平稳扰动满足交叉路口的属性，则证明了此类动作的局部刚性结果。我们还在保留一系列量的操作中给出了局部刚性结果。我们的方法主要使用KAM迭代方案的概括。
This paper studies local rigidity for some isometric toral extensions of partially hyperbolic $\mathbb{Z}^k$ ($k\geqslant 2$) actions on the torus. We prove a $C^\infty$ local rigidity result for such actions, provided that the smooth perturbations of the actions satisfy the intersection property. We also give a local rigidity result within a class of volume preserving actions. Our method mainly uses a generalization of the KAM iterative scheme.
