2004/05/03 by Dana Schlomiuk, Schlomiuk, Dana, Nicolae Vulpe +1
Engineering · Mathematics · #13A50 #34C05 #Advanced Differential Equations and Dynamical Systems #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:13A50 #msc:34C05
paper · pdf · doi:10.48550/arxiv.math/0405026
48 pages, 2 Postscript figures, Latex
arxiv created 2004/05/03 · openalex publication_date 2004/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.