Discontinuity growth of interval exchange maps
Discontinuity growth of interval exchange maps
复制标题
区间交换图的不连续增长
DOI：
10.3934/jmd.2009.3.379
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Christopher F. Novak
中科院分区：
文献类型：
--
作者：
Christopher F. Novak
对于区间交换映射，其迭代的不连续点的个数要么是线性增长的，要么是有界的。这个二分法被用来证明区间交换的群不包含失真元素，给出了不通过区间交换忠实行动的群的例子。作为这一二分法的进一步应用，给出了区间交换机群中中心化器的分类。中心化子的这种分类用于计算区间交换群的自同构群。
For an interval exchange map, the number of discontinuities of its iterates either exhibits linear growth or is bounded. This dichotomy is used to prove that the group of interval exchanges does not contain distortion elements, giving examples of groups that do not act faithfully via interval exchanges. As a further application of this dichotomy, a classification of centralizers in the group of interval exchanges is given. This classification of centralizers is used to compute the automorphism group of the interval exchange group.