Acta Scientiarum Naturalium Universitatis Pekinensis

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The Bifurcation Phenomena of Polycycle S(3) of Hamiltonian System Under Small Perturbations

LI Baoyi1, ZHANG Zhifen2   

  1. 1Department of Mathematics, Tianjin Normal University, Tianjin, 300073; 2School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:1997-06-19 Online:1998-09-20 Published:1998-09-20


李宝毅1, 张芷芬2   

  1. 1天津师范大学数学系,天津,300073; 2北京大学数学学院,北京,100871

Abstract: By means of finitely-smooth normal form theory and the method of infinitesimal analysis, it is proved that the cyclicity of polycycle S(3) of planar Hamiltonian system under small perturbations with certain nondegenerate condition is 3, thus the results of A.Mourtada about the cyclicity of isolated S(3) is generalized.

Key words: polycycle, cyclicity, finitely-smooth normal form

摘要: 利用Yu S Ilyashenko等人的有限光滑正规形理论,用无穷小分析的方法研究了平面Hamilton系统的奇异环S(3)在自治小扰动下的分歧现象,证明了在非退化条件下,S(3)的环性为3,推广了A.Mourtada关于孤立的奇异环S(3)的环性的结论。

关键词: 奇异环, 环性, 有限光滑正规形

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