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math.DS2018
On the computation of Darboux first integrals of a class of planar polynomial vector fields
A. Ferragut, C. Galindo, F. Monserrat
We study the class of planar polynomial vector fields admitting Darboux first integrals of the type , where the 's are positive real numbers and the $…
math.DS2008
On the characterization of algebraically integrable plane foliations
C. Galindo, F. Monserrat
We give a characterization theorem for non-degenerated plane foliations of degree different from 1 having a rational first integral. Moreover, we prove that the degree of a non…
math.DS2005
Algebraic Integrability of Foliations of the Plane
C. Galindo, F. Monserrat
We give an algorithm to decide whether an algebraic plane foliation F has a rational first integral and to compute it in the affirmative case. The algorithm runs whenever we assume…