UPPER BOUNDS FOR THE ASSOCIATED NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR TWO CLASSES OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE

DOI10.11948/2018.1959zbMath1477.34061OpenAlexW2902139717MaRDI QIDQ5148059

Xiaochun Hong, Yanjie Wang, Jun-Liang Lu

Publication date: 29 January 2021

Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11948/2018.1959

zbMATH Keywords

abelian integralweakened Hilbert's 16th problemquadratic reversible center

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) 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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (2)

Limit Cycles from Hopf Bifurcation in Nongeneric Quadratic Reversible Systems with Piecewise Perturbations ⋮ A LINEAR ESTIMATION TO THE NUMBER OF ZEROS FOR ABELIAN INTEGRALS IN A KIND OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE

Cites Work

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• Perturbations of quadratic centers of genus one
• Limit cycles of differential equations
• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
• On the abelian integrals of quadratic reversible centers with orbits formed by genus one curves of higher degree
• Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves
• Abelian integrals for quadratic centres having almost all their orbits formed by quartics*
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• LIMIT CYCLE BIFURCATIONS OF A KIND OF LIÉNARD SYSTEM WITH A HYPOBOLIC SADDLE AND A NILPOTENT CUSP

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