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 Zero bifurcation diagrams for Abelian integrals of some higher-order hyperelliptic Hamiltonian systems with three perturbation parameters Pei Yu,Xianbo Sun Keywords:Hyperelliptic Hamiltonian system; bifurcation diagram; Abelian integral Abstract: In this paper, we present the zero bifurcation diagrams for the Abelian integrals of two hyperelliptic Hamiltonian systems with three perturbation parameters using an algebraic-geometric approach. The method can be used to study the bifurcation diagrams for higher-order Hamiltonian systems with polynomial perturbations of any degree.