论文标题
引入二进制形式及其比率的同性动力学点
Introducing isodynamic points for binary forms and their ratios
论文作者
论文摘要
在Mobius组对三角形集合的作用下，众所周知，飞机三角形的同性动力点是其中心的唯一一对。概括了这个经典的结果，我们在下面介绍了与D度D度的单变量多项式相关的下面，至少3与双根最多为双根，一个多项式的2d-4（最多）2d-4的多项式，使得该图与Mobius组对初始多项式及其图像的零基因座的动作进行通勤。图像多项式的根部将称为映射多项式的同性动力学点。我们的构造自然从单变量的多项式到二元形式，再到其比率。
The isodynamic points of a plane triangle are known to be the only pair of its centers invariant under the action of the Mobius group on the set of triangles. Generalizing this classical result, we introduce below the isodynamic map associating to a univariate polynomial of degree d at least 3 with at most double roots a polynomial of degree (at most) 2d-4 such that this map commutes with the action of the Mobius group on the zero loci of the initial polynomial and its image. The roots of the image polynomial will be called the isodynamic points of the preimage polynomial. Our construction naturally extends from univariate polynomials to binary forms and further to their ratios.
