| 摘要: |
| 本文研究了一类十一次多中心平面Hamilton系统在n(n=4k+1;k∈N+)次多项式扰动下Abelian积分的零点个数.应用Picard-Fuchs方程法,证明了这类扰动Hamilton系统的Abelian积分的零点个数的上界(计重数). |
| 关键词: Hamilton系统 Abelian积分 Picard-Fuchs方程 极限环 |
| DOI： |
| 分类号:O175 |
| 基金项目:国家自然科学基金基金资助 (12261070);宁夏自然科学基金资助 (2022AAC03333). |
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| THE NUMBER OF ZEROS OF ABELIAN INTEGRALS OF A CLASS OF HAMILTONIAN SYSTEM WITH ELEVEN DEGREE |
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BAI Long, DONG Bai-Ying
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School of Mathematics and Computer Science, Ningxia Normal University, Guyuan Ningxia 756099, China
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| Abstract: |
| In this paper, we study the number of zeros of Abelian integral for a class of Hamiltonian system under perturbations of a polynomials with degree n(n=4k+1;k∈N+. By using Picard-Fuchs equation method, we derive the upper bound of the number of zeros of Abelian integrals for this class of perturbed Hamiltonian systems (taking into account the multiplicity). |
| Key words: Hamilton system Abelian integral Picard-Fuchs equation limit cycle |
