The theory of integrability plays an important role in the study of the dynamics of differential
systems. This theory is related to several branches of mathematics, such as algebraic …

We consider polynomial differential systems in the plane with Liouvillian first integrals. It is
shown that all such systems have Darbouxian integrating factors, and that the search for …

In the theory of ordinary differential equations we can distinguish two fundamental problems.
The first, which we may call the direct problem, is, in a broad sense, to find all solutions of a …

Algebraic aspects of integrability for polynomial systems — Universitat Autònoma de
Barcelona Research Portal Skip to main navigation Skip to search Skip to main content …

On the Darboux Integrability of Polynomial Differential Systems Page 1 Qual. Theory Dyn. Syst.
(2012) 11:129–144 DOI 10.1007/s12346-011-0053-x Qualitative Theory of Dynamical Systems …

In 1891, Poincaré started a series of three papers in which he tried to answer the following
question (cf.[21–23]):“Is it possible to decide if an algebraic differential equation in two …

Nonlinear ordinary differential equations appear in many branches of applied mathematics,
physics and, in general, in applied sciences. For a differential system or a vector field …

Application of the theory of the discriminant to highly singular plane curves Page 1 Math.
Proc. Camb. Phil. Soc. (1999), 126, 259 Printed in the United Kingdom # 1999 Cambridge …

We develop a study on local polar invariants of planar complex analytic foliations at (C2, 0),
which leads to the characterization of second type foliations and of generalized curve …

We present three main results. The first two provide sufficient conditions in order that a
planar polynomial vector field in C2 has a rational first integral, and the third one studies the …