发表机构
Institute of Mathematics NASU（乌克兰国家科学院数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广了带断点圆微分同胚的刚性结果，将时间反转对偶性从单个断点扩展到多个断点，引入偶数个线性分式映射的交换集合，并满足特定交换关系。
AI 中文摘要
线性分式旋转区间交换变换在利用重整化群方法研究带断点的圆微分同胚时自然出现。此前，我们通过建立相应线性分式映射交换对的时间反转对偶性，获得了关于带单个断点的圆微分同胚的一个重要刚性结果。在本文中，我们将已建立的对偶性推广到多个断点的情况，其中先前情况下的交换对被偶数个线性分式映射的“交换集合”所取代，这些映射按照特殊类型的旋转区间交换方案作用，同时满足某些交换关系。
英文摘要
Linear-fractional rotational interval exchange transformations appear naturally when investigating circle diffeomorphisms with breaks using the renormalization group approach. Earlier, we achieved an important rigidity result on circle diffeomorphisms with a single break by means of establishing a time-reversing duality for the corresponding commuting pairs of linear-fractional maps. In this paper, we extend the established duality to the case of multiple breaks, where a commuting pair from the previous case is replaced by a `commuting collection' of an even number of linear-fractional maps, which act according to a rotational interval exchange scheme of special type, while satisfying certain commutation relations.
