解读劳兹归纳法：对布费托夫一般问题的回答
Decoding Rauzy Induction: An Answer to Bufetov's General Question
摘要：
给定一个典型的区间交换变换，我们可以通过劳齐归纳法自然地将它与一个无穷序列矩阵联系起来。这些矩阵编码的诱导间隔内的原始交换变换的访问。2010年，W. A.维奇表明，这些矩阵足以恢复原来的区间交换变换，唯一的拓扑共轭，回答了一个问题。布费托夫在这项工作中，我们表明，区间交换变换可以恢复，是唯一的模共轭时，我们只知道这些矩阵的连续产品。这回答了A的另一个问题。布费托夫我们还将这一结果推广到任何产生平方访问矩阵的归纳方案。
英文摘要：
Given a typical interval exchange transformation, we may naturally associate to it an infinite sequence of matrices through Rauzy induction. These matrices encode visitations of the induced interval exchange transformations within the original. In 2010, W. A. Veech showed that these matrices suffice to recover the original interval exchange transformation, unique up to topological conjugacy, answering a question of A. Bufetov. In this work, we show that interval exchange transformation may be recovered and is unique modulo conjugacy when we instead only know consecutive products of these matrices. This answers another question of A. Bufetov. We also extend this result to any inductive scheme that produces square visitation matrices.
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