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| Global Phase Portraits of Symmetrical CubicHamiltonian Systems with a Nilpotent SingularPoint |
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| KeyWord:Hamiltonian systems nilpotent singular point global phase por-
traits Poincar´ e transformation |
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| Abstract: |
| Han et al. [Han et al., Polynomial Hamiltonian systems with a nilpotent critical point, J. Adv. Space Res. 2010, 46, 521–525] successfully
studied local behavior of an isolated nilpotent critical point for polynomial
Hamiltonian systems. In this paper, we extend the previous result by analyzing
the global phase portraits of polynomial Hamiltonian systems. We provide 12
non-topological equivalent classes of global phase portraits in the Poincar´ e disk of cubic polynomial Hamiltonian systems with a nilpotent center or saddle at origin under some conditions of symmetry. |
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