Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves

DOI10.1142/S0218127416500206zbMath1334.34080OpenAlexW2295372366MaRDI QIDQ2800707

Longwei Chen, Xiaochun Hong, Shaolong Xie

Publication date: 18 April 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127416500206

zbMATH Keywords

Abelian integralweakened 16th Hilbert problemquadratic reversible center

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (6)

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations ⋮ UPPER BOUNDS FOR THE ASSOCIATED NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR TWO CLASSES OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE ⋮ A class of reversible quadratic systems with piecewise polynomial perturbations ⋮ A LINEAR ESTIMATION TO THE NUMBER OF ZEROS FOR ABELIAN INTEGRALS IN A KIND OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE ⋮ Limit cycles in two kinds of quadratic reversible systems with non-smooth perturbations

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