大型分叉支座
Large bifurcation supports
摘要：
在研究$S^2$上向量场的全局分支时，区分一个“分支实际发生的地方”--分支支集是很重要的。希望只研究支集附近的分歧就足够了。分歧支撑的第一个定义是由V. Arnold提出的。但这一套似乎太小了。特别是，新发现的效果，在$S^2$上的三参数家庭的空间中的一个开域，没有结构稳定的家庭，是不可见的分支支持的附近。在这篇文章中，我们给出了一个新的定义“大分歧支持”，完成任务。粗略地说，如果我们知道一个向量场的相图的拓扑型，并且我们也知道在大分歧支撑的一个邻域内的分歧，那么我们就知道在整个球面上的分歧。
英文摘要：
In the study of global bifurcations of vector fields on $S^2$, it is important to distinguish a set "where the bifurcation actually occurs", -- the bifurcation support. Hopefully, it is sufficient to study the bifurcation in a neighborhood of the support only. The first definition of bifurcation support was proposed by V.Arnold. However this set appears to be too small. In particular, the newly discovered effect, an open domain in the space of three-parametric families on $S^2$ with no structurally stable families, is not visible in a neighborhood of the bifurcation support. In this article, we give a new definition of "large bifurcation support" that accomplishes the task. Roughly speaking, if we know the topological type of the phase portrait of a vector field, and we also know the bifurcation in a neighborhood of the large bifurcation support, then we know the bifurcation on the whole sphere.
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