论文标题
部分可观测时空混沌系统的无模型预测
K-differentials with prescribed singularities
论文作者
论文摘要
我们研究了当地的不变性，即在$ g \ geq 0 $的riemann表面上的meromorphic $ k $ differention，对于$ k \ geq 3 $。这些本地不变的人包括零和电线杆的订单，以及波兰人的$ k $ sistidues。我们表明，对于给定的零订单模式，存在少数例外，具有原始的全态$ k $ - 差异为这些订单的零。在meromormorphic情况下，对于$ g \ geq 1 $，每个预期的元组都作为$ k $ sisidues的配置。另一方面，对于零属中的某些阶层，由于$ k $ -differential的$ k $ - 珍藏的配置，因此不会发生许多元素（达到同时缩放）。
We study the local invariants that a meromorphic $k$-differential on a Riemann surface of genus $g \geq 0$ can have for $k \geq 3$. These local invariants include the orders of zeros and poles, as well as the $k$-residues at the poles. We show that for a given pattern of orders of zeros, there exists, with a few exceptions, a primitive holomorphic $k$-differential having zeros of these orders. In the meromorphic case, for genus $g \geq 1$, every expected tuple appears as a configuration of $k$-residues. On the other hand, for certain strata in genus zero, finitely many tuples (up to simultaneous scaling) do not occur as configurations of $k$-residues for a $k$-differential.
