Structure of three-interval exchange transformations II: a combinatorial description of the tranjectories
Structure of three-interval exchange transformations II: a combinatorial description of the tranjectories
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三区间交换变换的结构 II：轨迹的组合描述
DOI：
10.1007/bf02893083
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
L. Zamboni
中科院分区：
文献类型：
--
作者：
S. Ferenczi;Charles Holton;L. Zamboni
我们描述了一个算法，用于生成符号序列的代码下的三个区间上的区间交换变换的点的轨道。该算法有两个组成部分。第一种是应用于间隔长度的算术除法算法。这种算术构造最初是由作者在早期的一篇论文中介绍的，可以看作是正则连分数的二维推广。第二个组成部分是一个组合算法，它产生的双特殊因素的相关的符号子移位作为一个函数的算术扩展。因此，我们得到了块复杂度为2n+1的序列的完整特征，这些序列是三个区间交换变换的轨道的自然编码，从而回答了Rauzy的一个老问题。
We describe an algorithm for generating the symbolic sequences which code the orbits of points under an interval exchange transformation on three intervals. The algorithm has two components. The first is an arithmetic division algorithm applied to the lengths of the intervals. This arithmetic construction was originally introduced by the authors in an earlier paper and may be viewed as a two-dimensional generalization of the regular continued fraction. The second component is a combinatorial algorithm which generates the bispecial factors of the associated symbolic subshift as a function of the arithmetic expansion. As a consequence, we obtain a complete characterization of those sequences of block complexity 2n+1 which are natural codings of orbits of three-interval exchange transformations, thereby answering an old question of Rauzy.