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Further study on Horozov-Iliev’s method of estimating the number of limit cycles

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Abstract

In the study of the number of limit cycles of near-Hamiltonian systems, the first order Melnikov function plays an important role. This paper aims to generalize Horozov-Iliev’s method to estimate the upper bound of the number of zeros of the function.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11931016 and 11771296) and Hunan Provincial Education Department (Grant No. 19C1898).

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Authors and Affiliations

  1. Department of Computer Science and Mathematics, Changsha University, Changsha, 410022, China

    Xiaoyan Chen

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Maoan Han

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  1. Xiaoyan Chen
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  2. Maoan Han
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Correspondence to Maoan Han.

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Chen, X., Han, M. Further study on Horozov-Iliev’s method of estimating the number of limit cycles. Sci. China Math. 65, 2255–2270 (2022). https://doi.org/10.1007/s11425-021-1933-7

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  • DOI: https://doi.org/10.1007/s11425-021-1933-7

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