We study Kakutani equivalence for products of some special flows over rotations with roof function smooth except a singularity at $0\in \mathbb {T}$ . We estimate the Kakutani invariant for products of these flows with different powers of singularities and rotations from a full measure set. As a corollary, we obtain a countable family of pairwise non-Kakutani equivalent products of special flows over rotations.

中文翻译：

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一些特殊流动产品的角谷等价旋转

我们研究了一些特殊流过旋转的产品的角谷等价性，屋顶函数平滑，除了 $0\in \mathbb {T}$ 处的奇点。我们从完整的测量集中估计了这些具有不同奇点和旋转幂的流的产品的角谷不变量。作为推论，我们获得了可数族的成对非角谷等价产品的特殊流动旋转。