Polynomial Hamiltonian systems with a nilpotent critical point |
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| Authors: | Maoan Han Chenggang Shu Junmin Yang Abraham C-L Chian |
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| Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;2. Key Lab for Astrophysics, Shanghai Normal University, Shanghai 200234, China;3. National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, 12227-010 Sao Jose dos Campos SP, Brazil |
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| Abstract: | The study of Hamiltonian systems is important for space physics and astrophysics. In this paper, we study local behavior of an isolated nilpotent critical point for polynomial Hamiltonian systems. We prove that there are exact three cases: a center, a cusp or a saddle. Then for quadratic and cubic Hamiltonian systems we obtain necessary and sufficient conditions for a nilpotent critical point to be a center, a cusp or a saddle. We also give phase portraits for these systems under some conditions of symmetry. |
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| Keywords: | Hamiltonian systems Space physics Astrophysics Nilpotent critical point Mathematics |
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