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Some properties of Melnikov functions near a cuspidal loop - MaRDI portal

Some properties of Melnikov functions near a cuspidal loop (Q6131285)

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scientific article; zbMATH DE number 7827579

Language	Label	Description	Also known as
English	Some properties of Melnikov functions near a cuspidal loop	scientific article; zbMATH DE number 7827579

Statements

scholarly article

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Some properties of Melnikov functions near a cuspidal loop (English)

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Science China. Mathematics

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publication date

4 April 2024

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zbMATH Keywords

Melnikov function

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nilpotent cusp

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limit cycle

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bifurcation

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/s11425-022-2124-7

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Limit cycle bifurcation by perturbing a cuspidal loop of order 2 in a Hamiltonian system

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The number of small-amplitude limit cycles of Liénard equations

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Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces

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On Hopf cyclicity of planar systems

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General study on limit cycle bifurcation near a double homoclinic loop

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Limit cycles near homoclinic and heteroclinic loops

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Normal forms, Melnikov functions and bifurcations of limit cycles

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Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system

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Centennial History of Hilbert's 16th Problem

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

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Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields

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Bifurcation of limit cycles from a heteroclinic loop with two cusps

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

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ON THE NUMBER OF LIMIT CYCLES FOR A QUINTIC LIÉNARD SYSTEM UNDER POLYNOMIAL PERTURBATIONS

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Limit cycles of the generalized polynomial Liénard differential equations

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Hopf and homoclinic bifurcations for near-Hamiltonian systems

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Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems

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Limit Cycle Bifurcations by Perturbing a Hamiltonian System with a Cuspidal Loop of Order m

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New lower bounds for the Hilbert number of polynomial systems of Liénard type

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Limit cycles of some polynomial Liénard systems

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Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order \(m\)

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Bifurcation of limit cycles in a cubic-order planar system around a nilpotent critical point

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Identifiers

Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S11425-022-2124-7

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Sitelinks

Mathematics(1 entry)

mardi Publication:6131285

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