Estimating the number of zeros of abelian integrals for the perturbed cubic \(Z_4\)-equivariant planar Hamiltonian system

DOI10.1142/s0218127423500852zbMath1546.37082MaRDI QIDQ6537721

Wen-tao Huang, Aiyong Chen, Yong-Hui Xia, Huiyang Zhang

Publication date: 14 May 2024

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

zbMATH Keywords

Hamiltonian systemabelian integralweakened Hilbert's 16th problem\(Z_4\)-equivariant system

Mathematics Subject Classification ID

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) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Equivariant dynamical systems (37C81)

Cites Work

• Upper bounds for the number of zeroes for some abelian integrals
• Bifurcation diagrams for Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• On the number of zeros of abelian integrals for a kind of quartic Hamiltonians
• New results on the study of \(Z_q\)-equivariant planar polynomial vector fields
• On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle
• A unified proof of the weakened Hilbert 16th problem for \(n=2\)
• On the number of limit cycles bifurcating from a non-global degenerated center
• Bifurcation of ten small-amplitude limit cycles by perturbing a quadratic Hamiltonian system with cubic polynomials
• On the number of zeros of Abelian integrals. A constructive solution of the infinitesimal Hilbert sixteenth problem
• A cubic system with thirteen limit cycles
• Quadratic perturbations of quadratic codimension-four centers
• Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles
• Elliptic integrals and their nonoscillation
• Bifurcations of limit cycles forming compound eyes in the cubic system
• Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
• The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles
• Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
• Linear estimate for the number of zeros of abelian integrals
• Periodic traveling waves in a generalized BBM equation with weak backward diffusion and dissipation terms
• On the algebraic structure and the number of zeros of abelian integral for a class of Hamiltonians with degenerate singularities
• Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7
• The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points
• Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
• Double exponential estimate for the number of zeros of complete Abelian integrals and rational envelopes of linear ordinary differential equations with an irreducible monodromy group
• On the algebraic structure of abelian integrals for a kind of perturbed cubic Hamiltonian systems
• Twelve limit cycles around a singular point in a planar cubic-degree polynomial system
• Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven
• Perturbation theory of a symmetric center within Liénard equations
• Vector fields with homogeneous nonlinearities and many limit cycles
• The cyclicity of period annuli of a class of quintic Hamiltonian systems
• Centers of quasi-homogeneous polynomial differential equations of degree three
• Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
• Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• Bifurcations of limit cycles in a \(Z_6\)-equivariant planar vector field of degree 5
• The monotonicity of the ratio of two Abelian integrals
• Global Existence and Uniqueness of Periodic Waves in a Population Model with Density-Dependent Migrations and Allee Effect
• BIFURCATION OF LIMIT CYCLES IN Z₁₀-EQUIVARIANT VECTOR FIELDS OF DEGREE 9
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems
• Estimate of the number of zeros of Abelian integrals for an elliptic Hamiltonian with figure-of-eight loop
• Centennial History of Hilbert's 16th Problem
• The cyclicity of period annuli of degenerate quadratic Hamiltonian systems with elliptic segment loops
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• INVESTIGATIONS OF BIFURCATIONS OF LIMIT CYCLES IN Z₂-EQUIVARIANT PLANAR VECTOR FIELDS OF DEGREE 5
• Remarks on 16th weak Hilbert problem forn 2*
• Polynomial systems: a lower bound for the Hilbert numbers
• The sharp bound on the number of zeros of Abelian integral for a perturbation of hyper-elliptic Hamiltonian system
• Cyclicity of a Class of Hamiltonian Systems under Perturbations of Piecewise Smooth Polynomials
• On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM
• Abelian integrals and limit cycles
• Abelian integrals and limit cycles
• The infinitesimal 16th Hilbert problem in the quadratic case
• Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles
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