Geometry of quadratic differential systems in the neighborhood of infinity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:215

Article

Schlomiuk, D ; Vulpe, N

关键词: Poincare compactification;    singular point;    phase portrait;    topological index;    intersection multiplicity;    linear group;    affine invariant;   

DOI  :  10.1016/j.jde.2004.11.001

来源: Elsevier

【 摘 要 】

In this article we give a complete global classification of the class QS(ess) of planar, essentially quadratic differential systems (i.e. defined by relatively prime polynomials and whose points at infinity are not all singular), according to their topological behavior in the vicinity of infinity. This class depends on 12 parameters but due to the action of the affine group and re-scaling of time, the family actually depends on five parameters. Our classification theorem (Theorem 7.1) gives us a complete dictionary connecting very simple integer-valued invariants which encode the geometry of the systems in the vicinity of infinity, with algebraic invariants and comitants which are a powerful tool for computer algebra computations helpful in the route to obtain the full topological classification of the class QS of all quadratic differential systems. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

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