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.
出处
《系统科学与数学》
CSCD
北大核心
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
