论文标题
矩阵Painlevé系统中的汉密尔顿减少
Hamiltonian reductions in Matrix Painlevé systems
论文作者
论文摘要
对于某些有限组$ g $的bäcklund变换，我们表明，$ g $ invariant配置的动态为$ n | g | $ calogero-painlevé粒子等于某些$ n $ n $ parkogero-pargogero-painlever-painlevé系统。我们还表明，$ g $ invariant子集的动态减少$ n | g | \ times n | g | $矩阵painlevé系统等于某些$ n \ times n $ n $矩阵painlevé系统。 $ g $组对应于painlevé方程的折叠转换。证明是基于哈密顿的减少。
For certain finite groups $G$ of Bäcklund transformations we show that the dynamics of $G$-invariant configurations of $n|G|$ Calogero--Painlevé particles is equivalent to certain $n$-particle Calogero--Painlevé system. We also show that the reduction of dynamics on $G$-invariant subset of $n|G|\times n|G|$ matrix Painlevé system is equivalent to certain $n\times n$ matrix Painlevé system. The groups $G$ correspond to folding transformations of Painlevé equations. The proofs are based on the Hamiltonian reductions.
