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

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 differe...

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Autores:
Rodríguez Contreras, Contreras
Reyes Linero, Alberto
Campo Donado, Maria
Acosta-Humánez, Primitivo B.
Tipo de recurso:
Fecha de publicación:
2020
Institución:
Universidad Simón Bolívar
Repositorio:
Repositorio Digital USB
Idioma:
eng
OAI Identifier:
oai:bonga.unisimon.edu.co:20.500.12442/6723
Acceso en línea:
https://hdl.handle.net/20.500.12442/6723
http://www.jsju.org/index.php/journal/article/view/674
Palabra 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
Rights
openAccess
License
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
Description
Summary: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