Study of the cyclicity of some degenerate graphics inside quadratic systems

DOI10.3934/CPAA.2009.8.1133zbMath1170.34020OpenAlexW2050445365MaRDI QIDQ1016654

Freddy Dumortier, Christiane Rousseau

Publication date: 6 May 2009

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2009.8.1133

zbMATH Keywords

singular perturbationsfinite cyclicitydegenerate graphics

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Local and nonlocal bifurcation theory for dynamical systems (37G99) Relaxation oscillations for ordinary differential equations (34C26)

Related Items (5)

Limit cycles near hyperbolas in quadratic systems ⋮ Cyclicity of degenerate graphic \(DF_{2a}\) of Dumortier-Roussarie-Rousseau program ⋮ Singular perturbations and vanishing passage through a turning point ⋮ The number of limit cycles for regularized piecewise polynomial systems is unbounded ⋮ Cyclicity of canard cycles with hyperbolic saddles located away from the critical curve

This page was built for publication: Study of the cyclicity of some degenerate graphics inside quadratic systems