Hamilton系统的奇异环S(3)在小扰动下的分歧现象

The Bifurcation Phenomena of Polycycle S(3) ofHamiltonian System Under Small Perturbations

利用ＹｕＳＩｌｙａｓｈｅｎｋｏ［１，２］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。

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.