Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems

2015/02/03 by Christiane Rousseau, Rousseau, Christiane, Chunhua Shan +3
Mathematics · #34C05 #34C07 (Primary) #37C10 #37G15 (Secondary) #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS #msc:34C05 #msc:34C07 #msc:37C10 #msc:37G15

paper · pdf · doi:10.48550/arxiv.1502.00689

18 pages, 7 figures

arxiv created 2015/02/03 · openalex publication_date 2015/02/03 · arxiv updated 2015/02/04 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper we show the finite cyclicity of the two graphics (I₁₂¹) and (I₁₃¹) through a triple nilpotent point of saddle type inside quadratic vector fields. These results contribute to the program launched in 1994 by Dumortier, Roussarie and Rousseau (DRR program) to show the existence of a uniform upper bound for the number of limit cycles for planar quadratic vector fields.

Related

• Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems
• Uniqueness of Limit Cycles for Quadratic Vector Fields
• Geometry of planar quadratic systems
• On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields
• On the configuration of limit cycles in planar vector fields