论文标题
具有两个焦点奇点的四参数半牙本系统的高度不变
The height invariant of a four-parameter semitoric system with two focus-focus singularities
论文作者
论文摘要
半牙本质系统是一类完全可以集成的系统，具有两个自由度，大约十年前，Pelayo和Vu NGOC在五个符合性不变性方面进行了符合分类。如果半牙本系统具有多种焦点奇异性，那么其中一些不变性具有多个组件，一个用于每个焦点对焦奇异性。他们的计算一点也不明显，尤其是在多参数家庭中。在本文中，我们考虑了一个具有两个焦点奇异性的半标准系统的四参数家族。特别是，除了多边形不变外，我们还计算了所谓的高度不变。此外，我们表明，此不变的两个组成部分以复杂的方式编码系统的对称性。
Semitoric systems are a special class of completely integrable systems with two degrees of freedom that have been symplectically classified by Pelayo and Vu Ngoc about a decade ago in terms of five symplectic invariants. If a semitoric system has several focus-focus singularities, then some of these invariants have multiple components, one for each focus-focus singularity. Their computation is not at all evident, especially in multi-parameter families. In this paper, we consider a four-parameter family of semitoric systems with two focus-focus singularities. In particular, apart from the polygon invariant, we compute the so-called height invariant. Moreover, we show that the two components of this invariant encode the symmetries of the system in an intricate way.
