标题： 关于六条直线某些排列上线性算子$Λ_{\{2\},\{3\}}$的动力学 显示英文标题

标题： On the dynamics of the line operator $Λ_{\{2\},\{3\}}$ on some arrangements of six lines

摘要： 算子$\Lambda_{\{2\},\{3\}}$在线排列上的作用是通过将一个线排列\mathcal{A}与包含\mathcal{A}的重叠点中恰好三个点的线的并集相关联来定义的。 我们说六条不相切于一条圆锥曲线的线形成一个无名排列，如果它们的并集的奇点只有双点，但其对偶线排列有六个三重点、六个五点和27个双点。 无名排列的模空间是一个点和一条线的并集。 算子$\Lambda_{\{2\},\{3\}}$对无名排列的图像仍然是一个无名排列。 我们研究算子$\Lambda_{\{2\},\{3\}}$在这些排列上的动力学，并得到周期性排列与线的Ceva排列有关。 显示英文摘要

摘要： The operator $\Lambda_{\{2\},\{3\}}$ acting on line arrangements is defined by associating to a line arrangement \mathcal{A}, the line arrangement which is the union of the lines containing exactly three points among the double points of \mathcal{A}. We say that six lines not tangent to a conic form an unassuming arrangement if the singularities of their union are only double points, but the dual line arrangement has six triple points, six 5-points and 27 double points. The moduli space of unassuming arrangements is the union of a point and a line. The image by the operator $\Lambda_{\{2\},\{3\}}$ of an unassuming arrangement is again an unassuming arrangement. We study the dynamics of the operator $\Lambda_{\{2\},\{3\}}$ on these arrangements and we obtain that the periodic arrangements are related to the Ceva arrangements of lines.