Cubic differential systems with invariant straight lines of total multiplicity eight and four distinct infinite singularities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:423

Article

Bujac, Cristina¹  Vulpe, Nicolae¹ 

[1] Moldavian Acad Sci, Inst Math & Comp Sci, Kishinev, Moldova

关键词: Cubic differential system;    Invariant line;    Singular point;    Configuration of invariant lines;    Croup action;    Affine invariant polynomial;   

DOI  :  10.1016/j.jmaa.2014.10.014

来源: Elsevier

【 摘 要 】

In this article we prove a classification theorem (Main Theorem) of real planar cubic vector fields which possess four distinct infinite singularities and eight invariant straight lines, including the line at infinity and including their multiplicities. This classification, which is taken modulo the action of the group of real affine transformations and time resealing, is given in terms of invariant polynomials. The algebraic invariants and cornitants allow one to verify for any given real cubic system with four infinite distinct singularities whether or not it has invariant lines of total multiplicity eight, and to specify its configuration of lines endowed with their corresponding real singularities of this system. The calculations can be implemented on computer. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free