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