| 双非线性化Toda特征值问题的Lie-Poisson结构 |
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| 引用本文： | 杜殿楼,郝艳红. 双非线性化Toda特征值问题的Lie-Poisson结构[J]. 郑州大学学报(理学版), 2005, 37(3): 1-6 |
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| 作者姓名： | 杜殿楼 郝艳红 |
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| 作者单位： | 郑州大学数学系,郑州,450001 |
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| 基金项目： | 国家自然科学基金，河南省教育厅自然科学基金 |
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| 摘 要： | 利用Hamilton对称群的作用不变量,将R4N上具有标准辛结构的双非线性化Toda特征值问题约化为R4N/(R＞0)N上Lie-Poisson结构下的3×3非线性化特征值问题;并进一步讨论了该3×3非线性化特征值问题与R2N上标准辛结构下的2×2非线性化特征值问题之间的关系.
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| 关 键 词： | 约化 Lie-Poisson结构 辛映射 Poisson映射 |
| 文章编号： | 1671-6841(2005)03-0001-06 |
| 收稿时间： | 2004-10-12 |
| 修稿时间： | 2004-10-12 |
Lie-Poisson Structure for the Binary Nonlinearized Toda Spectral Problem |
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| Du Dianlou,Hao Yanhong. Lie-Poisson Structure for the Binary Nonlinearized Toda Spectral Problem[J]. Journal of Zhengzhou University(Natrual Science Edition), 2005, 37(3): 1-6 |
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| Authors: | Du Dianlou Hao Yanhong |
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| Abstract: | Hamiltonian symmetry group (R＞0)N generated through a family of conserved integrals is proposed. Themethod of invariants is used to reduce the binary nonlinearized Toda spectral problem on R4N into a 3 × 3 nonlinearized spectral problem with a Lie-Poisson structure on R4N/(R＞0)N. Furthermore, it is shown that the 3 × 3 one restricted on the common level set of cones is a usual 2 × 2 mono-nonlinearized spectral problem. |
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| Keywords: | reduction Lie-Poisson structure symplectic map Poisson map |
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