2006/11/06 by Valery A. Gaiko, Gaiko, Valery A.
Computer Science · Mathematics · #34C05 #34C07 #34C23 #37G05 #37G10 #37G15 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematics and Applications #Polynomial and algebraic computation #math.CA #math.DS #msc:34C05 #msc:34C07 #msc:34C23 #msc:37G05 #msc:37G10 #msc:37G15
paper · pdf · doi:10.48550/arxiv.math/0611142
13 pages
arxiv created 2006/11/06 · openalex publication_date 2006/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert's Sixteenth Problem in this special case of polynomial systems is suggested. Using geometric properties of four field rotation parameters of a new canonical system which is constructed in this paper, we present a proof of our earlier conjecture that the maximum number of limit cycles in a quadratic system is equal to four and the only possible their distribution is (3:1). Besides, applying the Wintner-Perko termination principle for multiple limit cycles to our canonical system, we prove in a different way that a quadratic system has at most three limit cycles around a singular point (focus) and give another proof of the same conjecture.