Proof of two conjectures for perturbed piecewise linear Hamiltonian systems

In this paper, we study the number of limit cycles bifurcating from the centers of piecewise linear Hamiltonian systems having either a homoclinic loop or a heteroclinic loop under the perturbations of piecewise smooth polynomials. By investigating the Chebyshev properties of generating functions of...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 81; p. 104195
Main Authors Sui, Shiyou, Zhang, Yongkang, Li, Baoyi
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2025
Subjects
Chebyshev property
Limit cycle
Melnikov function
Piecewise smooth system
Melnikov function
Piecewise smooth system
Limit cycle
Chebyshev property
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Summary:In this paper, we study the number of limit cycles bifurcating from the centers of piecewise linear Hamiltonian systems having either a homoclinic loop or a heteroclinic loop under the perturbations of piecewise smooth polynomials. By investigating the Chebyshev properties of generating functions of the first order Melnikov functions, we obtain the sharp bounds of the number of limit cycles bifurcating from the periodic annuluses, which confirm the conjectures proposed by Liang, Han and Romanovski (2012) and Liang and Han (2016).
ISSN:1468-1218
DOI:10.1016/j.nonrwa.2024.104195