In this book we consider planar polynomial differential systems, ie systems of the form dx dt=
p (x, y), dy dt= q (x, y) where p (x, y), q (x, y) are polynomials in x, y with real coefficients. To …

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 …

The relation between limit cycles of planar differential systems and the inverse integrating
factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From …

This paper deals with planar piecewise linear refracting systems with a straight line of
separation. Using the Poincaré compactification, we provide the classification of the phase …

During the last forty years the theory of integrability of Darboux, in terms of algebraic
invariant curves of polynomial systems has been very much extended and it is now an active …

A New Algorithm for Finding Rational First Integrals of Polynomial Vector Fields Page 1 Qual.
Theory Dyn. Syst. (2010) 9:89–99 DOI 10.1007/s12346-010-0021-x Qualitative Theory of …

We describe the origin and evolution of ideas on topological and polynomial invariants and
their interaction, in problems of classification of polynomial vector fields. The concept of …

Let QSH be the family of non-degenerate planar quadratic differential systems possessing
an invariant hyperbola. We study this class from the viewpoint of integrability. This is a rich …

This paper deals with the global dynamics of planar piecewise smooth differential systems
constituted by two different vector fields separated by one straight line that passes through …

Planar quadratic differential systems occur in many areas of applied mathematics. Although
more than a thousand papers were written on these systems, a complete understanding of …