标题： 四阶Painlevé系统的初始值空间与$A_5^{(1)}\times A_1^{(1)}$对称性 显示英文标题

标题： Initial value space of the fourth order Painlevé system with $A_5^{(1)}\times A_1^{(1)}$ symmetry

摘要： Painlevé方程的初始值空间由Okamoto提出。它们是辛流形，在其中Painlevé方程被描述为所有坐标上的多项式哈密顿系统。在本文中，我们构建了一个具有类型$A_5^{(1)}\times A_1^{(1)}$仿射Weyl群对称性的四阶Painlevé系统的初始值空间。 显示英文摘要

摘要： The initial value spaces of the Painlev\'{e} equations are proposed by Okamoto. They are symplectic manifolds in which the Painlev\'{e} equations are described as polynomial Hamiltonian systems on all coordinates. In this article, we construct an initial value space of the fourth order Painlev\'{e} system with affine Weyl group symmetry of type $A_5^{(1)}\times A_1^{(1)}$.