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 …

In this article, we study the Lotka–Volterra planar quadratic differential systems. We denote
by LV systems all systems which can be brought to a Lotka–Volterra system by an affine …

The Lotka-Volterra planar quadratic differential systems have numerous applications but the
global study of this class proved to be a challenge difficult to handle. Indeed, the four …

In the topological classification of phase portraits no distinctions are made between a focus
and a node and neither are they made between a strong and a weak focus or between foci …

In Artés et al.(Geometric configurations of singularities of planar polynomial differential
systems. A global classification in the quadratic case. Birkhäuser, Basel, 2019) the authors …

This article is about weak singularities of quadratic differential systems, that is, non-
degenerate singular points with traces of the corresponding linearized systems at such …

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 …

Let QSH be the whole class of non-degenerate planar quadratic differential systems
possessing at least one invariant hyperbola. We classify this family of systems, modulo the …

Let QSL≥ i be the family of quadratic differential systems with invariant lines of total
multiplicity at least i and let QSL i denote the family of quadratic systems with invariant lines …

We classify all cubic differential systems with exactly seven invariant straight lines (taking
into account their parallel multiplicity) which form a configuration of type (3, 3, 1). We prove …