A NORMAL FORM OF HAMILTONIAN SYSTEMS OF SEVERAL TIME VARIABLES WITH A REGULAR SINGULARITY
A NORMAL FORM OF HAMILTONIAN SYSTEMS OF SEVERAL TIME VARIABLES WITH A REGULAR SINGULARITY
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具有正则奇异性的多时变量哈密顿系统的范式
DOI：
10.1006/jdeq.1996.0073
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发表时间：
1996
影响因子：
2.4
通讯作者：
K. Takano
中科院分区：
文献类型：
--
作者：
H. Kimura;Atusi Matumiya;K. Takano
在本文中，我们给出了某些哈密顿系统在多个时间变量中的局部约简定理，该定理适用于系统 Hn, n# N 在其固定奇点处的约简。为了解释这篇文章的目的，我们首先回顾一下系统 Hn 的基本原理，然后看看 Hn 减少时会发生什么。我们注意到 Hn 是第六 Painleve 微分方程到偏微分方程组的推广。系统 Hn 等效于 Garnier 系统 Gn，它是二阶线性常微分方程的单性保留变形方程的非线性系统，在复射影线 P1 上有 n+ 3 个正则奇异点和 n 个视奇异点（参见[14]）。在本文中，我们也将系统 Hn 称为卡尼尔系统。该系统的显式形式由下式给出：
In this note, we give a local reduction theorem for certain Hamiltonian systems in several time variables which is applicable to a reduction of the system Hn, n# N, at its fixed singular points. In order to explain the purpose of this note, we first review the fundamentals of the system Hn, and then see what happens in a reduction of Hn. We note that Hn is a generalization of the sixth Painleve differential equation to a system of partial differential equations.The system Hn is equivalent to the Garnier system Gn which is a nonlinear system of monodromy preserving deformation equations for a second order linear ordinary differential equation with n+ 3 regular singular points and n apparent singular points on the complex projective line P1 (see [14]). We call the system Hn also the Garnier system in this note. The explicit form of the system is given by the following: