We prove global smooth classification results for Anosov ℤ k actions on general compact manifolds, under certain irreduciblity conditions and the presence of sufficiently many Anosov elements. In particular, we remove all the uniform control assumptions which were used in all the previous results towards the Katok-Spatzier global rigidity conjecture on general manifolds. The main idea is to create a new mechanism labelled nonuniform redefining argument, to prove continuity of certain dynamically-defined objects. This leads to uniform control for higher-rank actions and should apply to more general rigidity problems in dynamical systems.

中文翻译：

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关于紧流形上高阶 Anosov 动作的分类

我们证明了 Anosov ℤ k 对一般紧凑流形的全局平滑分类结果，在某些不可约条件和足够多的 Anosov 元素的存在下。特别是，我们删除了所有先前在一般流形上的 Katok-Spatzier 全局刚度猜想的结果中使用的所有统一控制假设。主要思想是创建一种标记为非均匀重定义参数的新机制，以证明某些动态定义对象的连续性。这导致对更高阶动作的统一控制，并且应该适用于动力系统中更一般的刚性问题。