论文标题
间隔交换转换的差异属性和共轭类别
Discrepancy Properties and Conjugacy Classes of Interval Exchange Transformations
论文作者
论文摘要
间隔交换转换通常是唯一的千古地图，因此具有均匀分布的轨道。他们的统一程度可以根据星际票据来衡量。到目前为止，很少有具有低静止轨道的间隔交换转换的示例，并且仅以$ n = 2,3 $的间隔为止，有标准可以完全表征这些间隔交换转换。在本文中，表明具有低分配轨道是在地图组成下不变的一个不变的类别。在一定程度上，这种方法使我们能够将间隔交换转换与没有距离的轨道与没有的轨道区分。对于$ n = 4 $的间隔，分类几乎是完整的，唯一具有单型不变的$ρ=（4,3,2,1）$的例外情况。详细讨论了这种特殊的单构不变。
Interval exchange transformations are typically uniquely ergodic maps and therefore have uniformly distributed orbits. Their degree of uniformity can be measured in terms of the star-discrepancy. Few examples of interval exchange transformations with low-discrepancy orbits are known so far and only for $n=2,3$ intervals, there are criteria to completely characterize those interval exchange transformations. In this paper, it is shown that having low-discrepancy orbits is a conjugacy class invariant under composition of maps. To a certain extent, this approach allows us to distinguish interval exchange transformations with low-discrepancy orbits from those without. For $n=4$ intervals, the classification is almost complete with the only exceptional case having monodromy invariant $ρ= (4,3,2,1)$. This particular monodromy invariant is discussed in detail.
