Global bifurcation of Limit Cycles in a Family of multiparameter System

@article{Xiang2004GlobalBO,
  title={Global bifurcation of Limit Cycles in a Family of multiparameter System},
  author={Guanghui Xiang and Maoan Han},
  journal={I. J. Bifurcation and Chaos},
  year={2004},
  volume={14},
  pages={3325-3335}
}
where H, f , g are C∞ functions in a region G ⊂ R2, ε ∈ R is a small parameter and a ∈ D ⊂ R with D compact. For ε = 0, (1) becomes Hamiltonian with the Hamiltonian function H(x, y). Suppose there exists a constant H0 > 0 such that for 0 < h < H0, the equation H(x, y) = h defines a smooth closed curve Lh ⊂ G surrounding the origin and shrinking to the origin as h → 0. Hence H(0, 0) = 0 and for ε = 0 (1) has a center at the origin. Let 
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