非简单类型的半环可积系统
Semitoric systems of non-simple type
AI总结：
本文扩展半环可积系统理论至非简单类型，处理同一能量-动量水平集中多个秩零孤立奇点的情况。
摘要：
在可积系统中，四维空间中所谓的“半环”可积系统近年来引起了广泛关注，尤其是因为经典和量子力学中的基本例子已被不同研究团队识别为半环系统。然而，其中几个例子表现出原始理论未包含的特殊特征，即在同一能量-动量水平集中存在多个（即两个或更多）秩为零的孤立奇点。具有此性质的系统被称为非简单系统。本文将Pelayo和Vũ Ngoc的原始理论扩展到非简单系统。
英文摘要：
Within integrable systems, the class of so called "semitoric" integrable systems in dimension four has attracted a lot of attention in recent years, especially since fundamental examples from classical and quantum mechanics have been identified as semitoric by different groups of researchers. Several of these examples, however, show a particular trait not included in the original theory, that is, the presence of multiple (i.e. two or more) rank zero isolated singularities in the same energy-momentum level sets. Systems with this property are called non-simple. This paper extends the original theory of Pelayo and Vũ Ngoc to non-simple systems.
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