On the period function of reversible quadratic centers with their orbits inside quartics

DOI10.1016/j.na.2009.04.062zbMath1182.34059OpenAlexW1991586996MaRDI QIDQ732597

Haihua Liang, Yulin Zhao

Publication date: 9 October 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.04.062

zbMATH Keywords

monotonicityPicard-Fuchs equationsperiod functionAbelian integrals

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (7)

The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle ⋮ The cyclicity of quadratic reversible systems with a center of genus one and non-Morsean point ⋮ The cyclicity of a class of quadratic reversible system of genus one ⋮ A criticality result for polycycles in a family of quadratic reversible centers ⋮ Isolated periodic wave trains and local critical wave lengths for a nonlinear reaction-diffusion equation ⋮ New lower bound for the number of critical periods for planar polynomial systems ⋮ Algebraic and analytical tools for the study of the period function

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