Melnikov函数在中心处的可微性问题  

DIFFERENTIABILITY PROBLEM OF MELNIKOV FUNCTIONS AT A CENTER

作　　者：韩茂安[1] 王政[2] 

机构地区：[1]上海交通大学数学系,上海200030 [2]山东工程学院基础部,淄博255012

出　　处：《系统科学与数学》1997年第3期269-274,共6页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金

摘　　要：本文证明（一阶）Melnikov函数在初等中心处关于Hamilton量至少为二次可微，井且得到二阶Melnikov函数为二次可微的充要条件，最后举例说明文[3,4]所讨论的一类扰动系统的后继函数在中心处不是二阶可微的．It is proved in the present paper that the first order Melnikov function M1 (h) is twice differentiable at the center with respect to Hamiltonian value h. A necessary and sufficient condition for the second order Melnikov function M2 to be C2 at the center is obtained. Then it is illustrated that the succession function of the perturbed system discussed in [3, 4] is not C^2 at the center.

关 键 词：MELNIKOV函数 中心 可微性 平面解析系统 

分 类 号：O175.1[理学—数学]