论文标题
等级两个紫红色系统的单粒轨道有限轨道
Finite orbits of monodromies of rank two Fuchsian systems
论文作者
论文摘要
我们以五个$ 2 \ times 2 $矩阵分类了Fuchsian系统的单层轨道。给出了此结果的明确证明。我们已经提出了一个猜想，以$ 6 $或更多$ 2 \ times 2 $矩阵进行类似的分类。考虑因素不包括所有单构矩阵具有共同特征向量的情况。为了对紫红色系统的有限单粒进行分类，我们结合了本文开发的两种方法。第一个是一种感应方法：使用较小数量的单肌矩阵的有限轨道该方法允许构建此类轨道以进行大量矩阵。第二种方法是一种形式主义，用于以在共同的共轭方式下以不变的方式来表示单肌矩阵的元组，这将问题转化为一种形式，使人们只能使用有理数数。 本文开发的分类可以被视为Garnier系统代数解决方案分类的第一步。
We classified finite orbits of monodromies of the Fuchsian system for five $2\times 2$ matrices. The explicit proof of this result is given. We have proposed a conjecture for a similar classification for $6$ or more $2\times 2$ matrices. Cases in which all monodromy matrices have a common eigenvector are excluded from the consideration. To classify the finite monodromies of the Fuchsian system we combined two methods developed in this paper. The first is an induction method: using finite orbits of smaller number of monodromy matrices the method allows the construction of such orbits for bigger numbers of matrices. The second method is a formalism for representing the tuple of monodromy matrices in a way that is invariant under common conjugation way, this transforms the problem into a form that allows one to work with rational numbers only. The classification developed in this paper can be considered as the first step to a classification of algebraic solutions of the Garnier system.
