Loop Algebra Moment Maps and Hamiltonian Models for the Painleve Transcendants
Loop Algebra Moment Maps and Hamiltonian Models for the Painleve Transcendants
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Painleve 超越点的循环代数矩图和哈密顿模型
DOI：
10.1090/fic/007/06
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
M. Wisse
中科院分区：
文献类型：
--
作者：
J. Harnad;M. Wisse
在经典的R矩阵框架中，Painlev超越项下的同位单调形变被解释为循环代数的对偶中的非自治哈密顿系统.通过矩映射嵌入，展示了四维或六维辛向量空间上的正则坐标如何参数化某些有理共轭轨道.Painlev超越项下的哈密顿量是通过拉回谱不变量环的元素而得到的.这些被证明确定了基础辛向量空间中的简单哈密顿系统.
The isomonodromic deformations underlying the Painlev\'e transcendants are interpreted as nonautonomous Hamiltonian systems in the dual $\gR^*$ of a loop algebra $\tilde\grg$ in the classical $R$-matrix framework. It is shown how canonical coordinates on symplectic vector spaces of dimensions four or six parametrize certain rational coadjoint orbits in $\gR^*$ via a moment map embedding. The Hamiltonians underlying the Painlev\'e transcendants are obtained by pulling back elements of the ring of spectral invariants. These are shown to determine simple Hamiltonian systems within the underlying symplectic vector space.