
Dynamical and Algebraic Analysis of Planar Polynomial Vector Fields Linked to Orthogonal Polynomials
Author(s) -
Contreras Rodríguez Contreras,
Alberto Reyes Linero,
Maria Campo Donado,
Primitivo B. Acosta-Humánez
Publication year - 2020
Publication title -
xi'nan jiaotong daxue xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 21
ISSN - 0258-2724
DOI - 10.35741/issn.0258-2724.55.4.29
Subject(s) - mathematics , phase portrait , galois group , orthogonal polynomials , generic polynomial , algebra over a field , pure mathematics , polynomial , differential (mechanical device) , galois theory , differential galois theory , embedding problem , mathematical analysis , physics , nonlinear system , quantum mechanics , bifurcation , thermodynamics
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.