On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation

Hongxian Zhou; Wei Xu; Shuang Li; Ying Zhang

doi:10.1016/j.amc.2007.01.052

On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation

Hongxian Zhou, Wei Xu, Shuang Li, Ying Zhang

数学与统计学院

Northwestern Polytechnical University Xian

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C₉¹ ⊃ [C₁¹ + 2 (C₃² ⊃ 2 C₁²)]. These results in the paper are useful for the study of the weakened Hilbert's 16th problem.

源语言	英语
页（从-至）	490-499
页数	10
期刊	Applied Mathematics and Computation
卷	190
期	1
DOI	https://doi.org/10.1016/j.amc.2007.01.052
出版状态	已出版 - 1 7月 2007

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abstract = "This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C91 ⊃ [C11 + 2 (C32 ⊃ 2 C12)]. These results in the paper are useful for the study of the weakened Hilbert's 16th problem.",

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N2 - This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C91 ⊃ [C11 + 2 (C32 ⊃ 2 C12)]. These results in the paper are useful for the study of the weakened Hilbert's 16th problem.

AB - This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C91 ⊃ [C11 + 2 (C32 ⊃ 2 C12)]. These results in the paper are useful for the study of the weakened Hilbert's 16th problem.

KW - Bifurcation

KW - Detection functions

KW - Hamiltonian system

KW - Limit cycles

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On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation

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