On the abelian integrals of quadratic reversible centers with orbits formed by genus one curves of higher degree

DOI10.1016/j.jmaa.2015.03.068zbMath1326.34063OpenAlexW2012186664MaRDI QIDQ2347422

Xiaochun Hong, Rui Ma, Shaolong Xie

Publication date: 27 May 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.03.068

zbMATH Keywords

abelian integralweakened 16th Hilbert problemquadratic reversible center

Mathematics Subject Classification ID

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 (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

Cites Work

• Unnamed Item
• Upper bounds for the number of zeroes for some abelian integrals
• On the number of limit cycles of a perturbed cubic polynomial differential center
• Global bifurcation of limit cycles in a family of polynomial systems
• Limit cycles bifurcating from a perturbed quartic center
• Limit cycles appearing from the perturbation of a system with a multiple line of critical points
• Perturbations of quadratic centers of genus one
• On the number of limit cycles bifurcating from a non-global degenerated center
• Limit cycles of cubic polynomial vector fields via the averaging theory
• Limit cycles of differential equations
• The number of limit cycles of a quintic polynomial system with center
• Bifurcation of limit cycles from a polynomial non-global center
• Quadratic centers defining elliptic surfaces
• The number of limit cycles of a quintic polynomial system
• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
• Linear estimation of the number of zeros of abelian integral for some cubic isochronous centers
• Singular points and limit cycles of planar polynomial vector fields
• Limit cycles of a perturbed cubic polynomial differential center
• Linear estimate on the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics
• Abelian integrals for quadratic centres having almost all their orbits formed by quartics*
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• Linear estimate for the number of zeros of Abelian integrals for quadratic isochronous centres
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• GLOBAL BIFURCATION OF LIMIT CYCLES IN A FAMILY OF MULTIPARAMETER SYSTEM
• Polynomial systems: a lower bound for the Hilbert numbers
• Averaging analysis of a perturbated quadratic center

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