论文标题
部分可观测时空混沌系统的无模型预测
Conductors of Abhyankar-Moh semigroups of even degrees
论文作者
论文摘要
在他们关于平面中线嵌入的论文中，Abhyankar和MOH证明了重要的不平等，现在称为Abhyankar-MOH不等式，可以用与平面代数曲线的无限分支相关的半群来说明。 Barrolleta，GarcíaBarroso和P \ Loski研究了满足Abhyankar-Moh不平等的整数的半群，并将其称为Abhyankar-Moh Semigroups。他们用最大导体描述了这样的半群。在本文中，我们证明，对于均匀程度的Abhyankar-MOH半群，都可以实现所有可能的导体值。我们的证明是建设性的，明确描述了以给定价值作为导体的家庭。
In their paper on the embeddings of the line in the plane, Abhyankar and Moh proved an important inequality, now known as the Abhyankar-Moh inequality, which can be stated in terms of the semigroup associated with the branch at infinity of a plane algebraic curve. Barrolleta, García Barroso and P\loski studied the semigroups of integers satisfying the Abhyankar-Moh inequality and call them Abhyankar-Moh semigroups. They described such semigroups with the maximum conductor. In this paper we prove that all possible conductor values are achieved for the Abhyankar-Moh semigroups of even degree. Our proof is constructive, explicitly describing families that achieve a given value as its conductor.
