双非线性化Toda特征值问题的Lie-Poisson结构(英文)  

Lie-Poisson Structure for the Binary Nonlinearized Toda Spectral Problem

作　　者：杜殿楼[1] 郝艳红[1] 

机构地区：[1]郑州大学数学系,郑州450001

出　　处：《郑州大学学报（理学版）》2005年第3期1-6,共6页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目,编号10471132;河南省教育厅自然科学基金资助项目,编号2004110006.

摘　　要：利用H am ilton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T oda特征值问题约化为R4N/(R>0)N上L ie-Po iss on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.Hamiltonian symmetry group（R〉0）^N generated through a family of conserved integrals is proposed.The method of invariants is used to reduce the binary nonlinearized Toda spectral problem on R^4N into a 3×3 nonlinearized spectral problem with a Lie-Poisson structure on R^4N/（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.

关 键 词：约化 LIE-POISSON结构 辛映射 Poisson映射 

分 类 号：O175.7[理学—数学]