Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials

Rodríguez Contreras, Contreras; Reyes Linero, Alberto; Campo Donado, Maria; Acosta-Humánez, Primitivo B.

Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials

Archivos

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Fecha

2020-08

Autores

Rodríguez Contreras, Contreras

Reyes Linero, Alberto

Campo Donado, Maria

Acosta-Humánez, Primitivo B.

Editor

Southwest Jiaotong University

Resumen

In the present work, our goal is to establish a study of some families of quadratic polynomial vector fields connected to orthogonal polynomials that relate, via two different points of view, the qualitative and the algebraic ones. We extend those results that contain some details related to differential Galois theory as well as the inclusion of Darboux theory of integrability and the qualitative theory of dynamical systems. We conclude this study with the construction of differential Galois groups, the calculation of Darboux first integral, and the construction of the global phase portraits
在当前的工作中，我们的目标是建立与正交多项式相关的二次多项式矢量场的一些族的研究，该正交多项式通过两种不同的观点相互关联，即定性和代数。我们扩展了这些结果，这些结果包含与微分加洛瓦理论有关的一些细节，以及包含达布可积性理论和动力学系统的定性理论。我们以差分伽罗瓦群的构造，达布克斯第一积分的计算以及整体相像的构造来结束本研究。

Palabras clave

Darboux first integral, Differential galois theory, Integrability, Orthogonal polynomial, Polynomials vector fields, 达布第一积分, 微分伽罗瓦理论, 可积性, 正交多项式, 多项式矢量场