| 非齐次Hamilton系统的Birkhoff表示 |
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| 引用本文： | 刘畅,宋端,刘世兴,郭永新.非齐次Hamilton系统的Birkhoff表示[J].中国科学(G辑),2013(4):541-548. |
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| 作者姓名： | 刘畅 宋端 刘世兴 郭永新 |
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| 作者单位： | [1]辽宁大学物理学院,沈阳110036 [2]北京理工大学宇航学院,北京100081 [3]辽东学院影像物理教研室,丹东118001 |
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| 基金项目： | 国家自然科学基金（批准号：11202090,11172120,10932002和10972127）、辽宁省重点实验室建设项目（批准号：2008403009）资助 |
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| 摘 要： | 本文首先讨论了Hamilton系统与Birkhoff系统的关系，以及Birkhoff系统研究的理论意义和实际价值．进一步研究了非齐次Hamilton系统的Birkhoff化理论、Birkhoff方程的实现条件、构造方法，指出了Birkhoff动力学研究的主要困难和未来应该重点关注的基本问题；最后给出了广义Birkhoff系统动力学方程的形式以及研究广义Birkhoff方程的重要意义，并探讨了赝广义Birkhoff方程的形式以及构造动力学系统赝广义Birkhoff方程的目的和意义．
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| 关 键 词： | 非齐次Hamilton系统 Birkhoff系统 Cauchy—Kovalevski定理 广义Birkhoff系统 赝广义 |
Birkhoffian representation of non-homogenous hamiltonian systems |
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| Authors: | LIU Chang SONG Duan LIU Shixing ＆ GUO Yongxin |
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| Institution: | 1 College of Physics, Liaoning University, Shenyang 110036, China; 2 School of Aerospace Engmeermg, Bezjzng lnstttute of Technology, Beijing 100081, China; 3 Physics of medical imaging department, Eastern Liaoning University, Dandong 118001, China) |
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| Abstract: | The relation between Hamiltonian system and Birkhoffian system is discussed in this article. Simultaneously, the theory significance and the practical value of Birkhoffian dynamical systems are also investigated. Furthermore, the Birkhoffian realization theory and methods for constructing Birkhoff＇s equation are also studied. Then the primary difficulty and the important investigative directions of Birkhoffian dynamics are pointed out in this article. Finally, the formulations and the significance of generalized Birkhoffian dynamics are given. At the same time the almost-generalized Birkhoff＇s equations and its applications are also discussed in briefly. |
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| Keywords: | Non-homogenous Hamiltonian system Birkhoffian system Cauchy-Kovalevski theorem generalizedBirkhoffian system almost-generalized Birkhoffian system |
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