无穷邻域内二次微分系统的几何
Geometry of quadratic differential systems in the neighbourhood of infinity
摘要：
本文考虑一类全平面二次微分系统在无穷远点附近的行为。这个族依赖于12个参数，但由于仿射群的作用和时间的重新缩放，该族实际上依赖于5个参数。我们给出了简单的，整数值的几何不变量，这个群作用这类家庭根据他们的相图在无穷大附近的拓扑结构。对于得到的每一个类，我们给出了代数不变式和伴随式的充要条件，以便能够很容易地检索任何系统，在任何图表中，几何以及系统在无穷大附近的动态特性。编制了计算机计算程序。
英文摘要：
In this article we consider the behavior in the vicinity of infinity of the class of all planar quadratic differential systems. This family depends on twelve parameters but due to action of the affine group and re-scaling of time the family actually depends on five parameters. We give simple, integer-valued geometric invariants for this group action which classify this family according to the topology of their phase portraits in the vicinity of infinity. For each one of the classes obtained we give necessary and sufficient conditions in terms of algebraic invariants and comitants so as to be able to easily retrieve for any system, in any chart, the geometric as well as the dynamic characteristics of the systems in the neighborhood of infinity. A program was implemented for computer calculations.
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