Polynomial Lemniscates and Their Fingerprints: From Geometry to Topology
Polynomial Lemniscates and Their Fingerprints: From Geometry to Topology
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多项式双纽线及其指纹：从几何到拓扑
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
A. Vasil’ev
中科院分区：
文献类型：
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作者：
A. Frolova;D. Khavinson;A. Vasil’ev
我们研究多项式双纽线的形状，和他们的指纹。我们重点关注指纹的拐点、它们的数量和几何意义。此外，我们研究了双纽线通用多项式的零的动态和它们的“爆炸”，通过在某个时刻将额外的零植入定义多项式中，然后研究所产生的变形。我们称之为动态多项式烟花，并表明它可以实现一个非酉操作数的建设。
We study shapes given by polynomial lemniscates, and their fingerprints. We focus on the inflection points of fingerprints, their number and geometric meaning. Furthermore, we study dynamics of zeros of lemniscate-generic polynomials and their ‘explosions’ that occur by planting additional zeros into a defining polynomial at a certain moment, and then studying the resulting deformation. We call this dynamics polynomial fireworks and show that it can be realized by a construction of a non-unitary operad.