| Volume 10, Number 6, 2020, Pages 2734-2755 DOI：10.11948/20200168 |
| Zero bifurcation diagrams for Abelian integrals: A study on higher-order hyperelliptic Hamiltonian systems with three perturbation parameters |
| Xianbo Sun,Pei Yu |
| 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. |
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