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 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

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