| 泊松流形中的一般哈密尔顿系统 |
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| 引用本文： | 王红.泊松流形中的一般哈密尔顿系统[J].太原理工大学学报,2005,36(6):738-741. |
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| 作者姓名： | 王红 |
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| 作者单位： | College of Mathematics and LPMC，Nankai University，Tianjin 300071，China |
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| 基金项目： | NaturalScienceFoundationofTianjin(05YFJMJC01200) |
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| 摘 要： | Symplectic geometryis one of the most i mpor-tant research subjects.In particular,the investiga-tion of the symplectic structures and the Poissonbrackets are closely related to the analytic mechan-ics.Nowadays,the symplectic method has been oneof the most i mportant toolsinthe study of dynami-cal systems1-6].On the other hand,the(general-ized)Hamiltonian systemis one of the most i mpor-tant research fields in nonlinear sciences,which isdirectly related to astronomical mechanics,aero-nautical…
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| 关 键 词： | 泊松流形 哈密尔顿系统 支架 泊松映射 向量场 |
| 文章编号： | 1007-9432（2005）06-0738-04 |
| 收稿时间： | 2005-07-02 |
| 修稿时间： | 2005年7月2日 |
Generalized Hamiltonian Systems on a Poisson Product Manifold |
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| WANG Hong.Generalized Hamiltonian Systems on a Poisson Product Manifold[J].Journal of Taiyuan University of Technology,2005,36(6):738-741. |
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| Authors: | WANG Hong |
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| Institution: | College of Mathematics and LPMC,Nankai University,Tianjin 300071,China |
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| Abstract: | We firstly intoruduced a kind of special functions and a kind of special Poisson bracket on a product manifold,then give a kind of special generalized Hamiltonian vector fields by using the special Poisson bracket.Moreover,we give a method to compose a new generalized Hamiltonian system on the Poisson product manifold by using two known generalized Hamitonian systems on the factor Poisson manifolds.We also discuss the conservative properties of the new composed generalized Hamiltonian systems as well as the relation between the Poisson mapping on the Poisson product manifold and that on the factor Poisson manifolds. |
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| Keywords: | poisson bracket poisson product manifold generalized Hamiltonian system poisson mapping |
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