Estimating the number of zeros of abelian integrals for the perturbed cubic \(Z_4\)-equivariant planar Hamiltonian system (Q6537721)

scientific article; zbMATH DE number 7847369

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English	Estimating the number of zeros of abelian integrals for the perturbed cubic \(Z_4\)-equivariant planar Hamiltonian system	scientific article; zbMATH DE number 7847369

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instance of

scholarly article

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title

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

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International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

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publication date

14 May 2024

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zbMATH Keywords

Hamiltonian system

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abelian integral

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weakened Hilbert's 16th problem

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\(Z_4\)-equivariant system

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Centers of quasi-homogeneous polynomial differential equations of degree three

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On the number of zeros of Abelian integrals. A constructive solution of the infinitesimal Hilbert sixteenth problem

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A unified proof of the weakened Hilbert 16th problem for \(n=2\)

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The cyclicity of period annuli of degenerate quadratic Hamiltonian systems with elliptic segment loops

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Polynomial systems: a lower bound for the Hilbert numbers

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Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields

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Bifurcation diagrams for Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields

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Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields

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Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

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Perturbation from an elliptic Hamiltonian of degree four. III: global centre.

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Abelian integrals and limit cycles

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Perturbation theory of a symmetric center within Liénard equations

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On the number of limit cycles bifurcating from a non-global degenerated center

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Upper bounds for the number of zeroes for some abelian integrals

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Vector fields with homogeneous nonlinearities and many limit cycles

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The infinitesimal 16th Hilbert problem in the quadratic case

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Quadratic perturbations of quadratic codimension-four centers

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On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems

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Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians

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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

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Centennial History of Hilbert's 16th Problem

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The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles

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Bifurcations of limit cycles forming compound eyes in the cubic system

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Q3831287

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Remarks on 16th weak Hilbert problem forn 2*

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Bifurcations of limit cycles in a \(Z_6\)-equivariant planar vector field of degree 5

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INVESTIGATIONS OF BIFURCATIONS OF LIMIT CYCLES IN Z2-EQUIVARIANT PLANAR VECTOR FIELDS OF DEGREE 5

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HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

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Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7

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A cubic system with thirteen limit cycles

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New results on the study of \(Z_q\)-equivariant planar polynomial vector fields

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Abelian integrals and limit cycles

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Estimate of the number of zeros of Abelian integrals for an elliptic Hamiltonian with figure-of-eight loop

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The monotonicity of the ratio of two abelian integrals

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Linear estimate for the number of zeros of abelian integrals

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Elliptic integrals and their nonoscillation

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Q3868118

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Q5409591

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The sharp bound on the number of zeros of Abelian integral for a perturbation of hyper-elliptic Hamiltonian system

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Global Existence and Uniqueness of Periodic Waves in a Population Model with Density-Dependent Migrations and Allee Effect

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Periodic traveling waves in a generalized BBM equation with weak backward diffusion and dissipation terms

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Bifurcation of ten small-amplitude limit cycles by perturbing a quadratic Hamiltonian system with cubic polynomials

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Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles

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BIFURCATION OF LIMIT CYCLES IN Z10-EQUIVARIANT VECTOR FIELDS OF DEGREE 9

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On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle

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On the number of zeros of abelian integrals for a kind of quartic Hamiltonians

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The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points

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On the algebraic structure and the number of zeros of abelian integral for a class of Hamiltonians with degenerate singularities

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On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems

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Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven

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TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM

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Twelve limit cycles around a singular point in a planar cubic-degree polynomial system

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Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians

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The cyclicity of period annuli of a class of quintic Hamiltonian systems

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On the algebraic structure of abelian integrals for a kind of perturbed cubic Hamiltonian systems

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Cyclicity of a Class of Hamiltonian Systems under Perturbations of Piecewise Smooth Polynomials

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Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type

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Identifiers

zbMATH Open document ID

1546.37082

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Mathematics Subject Classification ID

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10.1142/S0218127423500852

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Sitelinks

Mathematics(1 entry)

mardi Publication:6537721