HIGH-ORDER MELNIKOV FUNCTIONS AND THE PROBLEM OF UNIFORMITY IN GLOBAL BIFURCATION

In studying bifurcation of Hamiltonian system with small perturbation, it can not always be obtained the uniqueness of limit cycle uniformly for 0 < epsilon much less than 1 from monotonicity of I2 (h)/I1 (h), in case the first order Melnikov function M1 (h) = muI1 (h) + nuI2 (h) is degenerate at the end points of the interval of its definition. In this paper two examples have been constructed for showing the above conclusion.Mathematics, AppliedMathematicsSCI(E)10ARTICLE181-21216