二次域上的正则区间交换变换
Regular Interval Exchange Transformations over a Quadratic Field
摘要：
我们描述了一个推广的结果Boshernitzan和卡罗尔：一个扩展的拉格朗日定理的连续分数扩展的二次无理区间交换变换。为了做到这一点，我们使用一个双边版本的劳兹归纳法。特别地，我们证明了从长度定义在二次域上的区间交换变换出发，应用双侧Rauzy归纳法，只能得到有限个新的变换，直到同构。
英文摘要：
We describe a generalization of a result of Boshernitzan and Carroll: an extension of Lagrange's Theorem on continued fraction expansion of quadratic irrationals to interval exchange transformations. In order to do this, we use a two-sided version of the Rauzy induction. In particular, we show that starting from an interval exchange transforma- tion whose lengths are defined over a quadratic field and applying the two-sided Rauzy induction, one can obtain only a finite number of new transformations up to homothety.
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