Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center (Q1735089)

scientific article; zbMATH DE number 7043803

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English	Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center	scientific article; zbMATH DE number 7043803

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instance of

scholarly article

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title

Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center (English)

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Applied Mathematics and Computation

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publication date

28 March 2019

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zbMATH Keywords

near-Hamiltonian system

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nilpotent center

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Hopf bifurcation

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limit cycle

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normal form

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generalized Lyapunov constant

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MaRDI profile type

Publication

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full work available at URL

https://doi.org/10.1016/j.amc.2016.11.021

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cites work

The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale

0 references

Normal forms, Melnikov functions and bifurcations of limit cycles

0 references

Conditions for transient viremia in deterministic in-host models: viral blips need no exogenous trigger

0 references

Viral Blips May Not Need a Trigger: How Transient Viremia Can Arise in Deterministic In-Host Models

0 references

Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence

0 references

Mathematical problems for the next century

0 references

Introduction to analyzable functions and constructive proof of the Dulac conjecture

0 references

Q3868118

0 references

Q3871220

0 references

FOUR LIMIT CYCLES FROM PERTURBING QUADRATIC INTEGRABLE SYSTEMS BY QUADRATIC POLYNOMIALS

0 references

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

0 references

A cubic system with thirteen limit cycles

0 references

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

0 references

Nonlinear oscillations, dynamical systems, and bifurcations of vector fields

0 references

Q4744562

0 references

Q5809392

0 references

A Cubic System with Eight Small-Amplitude Limit Cycles

0 references

A cubic system with eight small-amplitude limit cycles

0 references

Symbolic computation of limit cycles associated with Hilbert's 16th problem

0 references

An application of regular chain theory to the study of limit cycles

0 references

Q5496558

0 references

Eleven small limit cycles in a cubic vector field

0 references

Q5474767

0 references

On a Żołądek theorem

0 references

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

0 references

Q5496427

0 references

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

0 references

Degenerate Hopf Bifurcation Formulas and Hilbert’s 16th Problem

0 references

Computation of normal forms via a perturbation technique

0 references

Q4768040

0 references

On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields

0 references

A new approach to the computation of the Lyapunov constants

0 references

An explicit recursive formula for computing the normal form and center manifold of general \(n\)-dimensional differential systems associated with Hopf bifurcations

0 references

An explicit recursive formula for computing the normal forms associated with semisimple cases

0 references

Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields

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MONODROMY AND STABILITY FOR NILPOTENT CRITICAL POINTS

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Local analytic integrability for nilpotent centers

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Symétrie et forme normale des centres et foyers dégénérés

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The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems

0 references

The center problem for a family of systems of differential equations having a nilpotent singular point

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Analytic nilpotent centers as limits of nondegenerate centers revisited

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Generating limit cycles from a nilpotent critical point via normal forms

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Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point

0 references

Singularities of vector fields

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Reversibility and classification of nilpotent centers

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The center-focus problem and reversibility

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Limit cycle bifurcations from a nilpotent focus or center of planar systems

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BIFURCATIONS OF LIMIT CYCLES AND CENTER PROBLEM FOR A CLASS OF CUBIC NILPOTENT SYSTEM

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LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER

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HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS

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COMPUTATION OF SIMPLEST NORMAL FORMS OF DIFFERENTIAL EQUATIONS ASSOCIATED WITH A DOUBLE-ZERO EIGENVALUE

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AN EFFICIENT METHOD FOR COMPUTING THE SIMPLEST NORMAL FORMS OF VECTOR FIELDS

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A matching pursuit technique for computing the simplest normal forms of vector fields

0 references

Bifurcation of limit cycles in 3rd-order \(Z_2\) Hamiltonian planar vector fields with 3rd-order perturbations

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Identifiers

zbMATH Open document ID

1411.34046

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Mathematics Subject Classification ID

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10.1016/J.AMC.2016.11.021

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Sitelinks

Mathematics(1 entry)

mardi Publication:1735089