Degree counting for Toda system with simple singularity: One point blow up
Degree counting for Toda system with simple singularity: One point blow up
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具有简单奇点的 Toda 系统的度数计算：一点爆炸
DOI：
10.1016/j.jde.2019.09.016
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发表时间：
2020
影响因子：
2.4
通讯作者：
Zhang Lei
中科院分区：
文献类型：
--
作者：
Lee Youngae;Lin Chang-Shou;Yang Wen;Zhang Lei
本文研究了当ρ 1∈(0,4 π)∪(4 π, 8 π)且ρ 2∈4π n时，具有简单奇异源的二阶Toda系统的阶数计算公式，关键的一步是推导出阴影系统的阶数计算公式，该公式由ρ 1趋于4π时的冒泡解推导而来。为了计算阴影系统的拓扑度，我们需要找到一些合适的变形。在这种变形过程中，我们将处理由这种现象引起的新困难：爆炸并不一定意味着质量的集中。这种现象的发生是由于奇点的坍缩。这是先前工作[25]的延续。
In this paper, we study the degree counting formula of the rank two Toda system with simple singular source when ρ 1∈(0, 4 π)∪(4 π, 8 π) and ρ 2∉ 4 π N. The key step is to derive the degree formula of the shadow system, which arises from the bubbling solutions as ρ 1 tends to 4π. In order to compute the topological degree of the shadow system, we need to find some suitable deformation. During this deformation, we shall deal with new difficulty arising from the phenomenon: blow up does not necessarily imply concentration of mass. This phenomenon occurs due to the collapsing of singularities. This is a continuation of the previous work [25].