THE FIRST THREE ORDER MELNIKOV FUNCTIONS FOR GENERAL PIECEWISE HAMILTONIAN SYSTEMS WITH A NON-REGULAR SEPARATION LINE

Peixing Yang; Jiang Yu

doi:10.11948/20230158

2024 Volume 14 Issue 3

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Peixing Yang, Jiang Yu. THE FIRST THREE ORDER MELNIKOV FUNCTIONS FOR GENERAL PIECEWISE HAMILTONIAN SYSTEMS WITH A NON-REGULAR SEPARATION LINE[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1374-1394. doi: 10.11948/20230158

Citation:

Peixing Yang, Jiang Yu. THE FIRST THREE ORDER MELNIKOV FUNCTIONS FOR GENERAL PIECEWISE HAMILTONIAN SYSTEMS WITH A NON-REGULAR SEPARATION LINE[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1374-1394. doi: 10.11948/20230158

THE FIRST THREE ORDER MELNIKOV FUNCTIONS FOR GENERAL PIECEWISE HAMILTONIAN SYSTEMS WITH A NON-REGULAR SEPARATION LINE

Peixing Yang^1, ,,
Jiang Yu^1,

1.
School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai 200240, China

Author Bio: Email: jiangyu@sjtu.edu.cn(J. Yu)
Corresponding author: Email: peixing0806@sjtu.edu.cn(P. Yang)

Abstract

Abstract

This paper focuses on the first three order Melnikov functions of general planar piecewise Hamiltonian systems under the piecewise perturbations with a non-regular separation line. By using the first three order Melnikov functions, we obtain the exact upper bounds of the number of limit cycles bifurcated from two different piecewise linear near-Hamiltonian systems.
- Melnikov functions /
- separation line /
- limit cycles
MSC: 34C05, 34C07, 37G15

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References

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