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DIFFERENTIABILITY PROBLEM OF MELNIKOV FUNCTIONS AT A CENTER
Melnikov函数在中心处的可微性问题

Keywords: Melnikov function,center,differentiability
Melnikov函数
,中心,可微性

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Abstract:

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.

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