[HTML][HTML] On the computation of Darboux first integrals of a class of planar polynomial vector fields
We study the class of planar polynomial vector fields admitting Darboux first integrals of the
type∏ i= 1 rfi α i, where the α i's are positive real numbers and the fi's are polynomials …
type∏ i= 1 rfi α i, where the α i's are positive real numbers and the fi's are polynomials …
Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces
C Galindo, F Monserrat, E Pérez-Callejo - Qualitative Theory of Dynamical …, 2022 - Springer
We study algebraic integrability of complex planar polynomial vector fields X= A (x, y)(∂/∂
x)+ B (x, y)(∂/∂ y) through extensions to Hirzebruch surfaces. Using these extensions, each …
x)+ B (x, y)(∂/∂ y) through extensions to Hirzebruch surfaces. Using these extensions, each …
Algebraic integrability with bounded genus
C Galindo, F Monserrat, E Pérez-Callejo - arXiv preprint arXiv:2401.09397, 2024 - arxiv.org
We provide an algorithm which decides whether a polynomial foliation $\mathcal
{F}^{\mathbb {C}^ 2} $ on the complex plane has a polynomial first integral of genus $ g\neq …
{F}^{\mathbb {C}^ 2} $ on the complex plane has a polynomial first integral of genus $ g\neq …
Catching Tangent Curves in Fields of Lines
SC Coutinho - The American Mathematical Monthly, 2021 - Taylor & Francis
Abstract In 1878, Gaston Darboux published a method for finding first integrals of differential
systems with polynomial coefficients. Combined with tools from algebraic geometry and …
systems with polynomial coefficients. Combined with tools from algebraic geometry and …
Invariant algebraic surfaces of polynomial vector fields in dimension three
We discuss criteria for the nonexistence, existence and computation of invariant algebraic
surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical …
surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical …