## Summary

In studying bifurcation of Hamiltonian system with small perturbation, it can not always be obtained the uniqueness of limit cycle uniformly for*0 < ε ≪ 1* from monotonicity of I_{2}(h)/I_{1}(h), in case the first order Melnikov function M_{1}(h)=μI_{1}(h) + vI_{2}(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.

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This work was partially supported by Natural Science Foundation of China.

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### Cite this article

Zhi-Fen, Z., Bao-Yi, L. High order Melnikov functions and the problem of uniformity in global bifurcation.
*Annali di Matematica* **161, **181–212 (1992). https://doi.org/10.1007/BF01759638

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### Keywords

- Periodic Orbit
- Hamiltonian System
- Homoclinic Orbit
- Closed Orbit
- Lower Order Term