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 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 …

A center p of a differential system in R^ 2 R 2 is global if R^ 2 ∖ {p\} R 2 {p is filled of periodic
orbits. It is known that a polynomial differential system of degree 2 has no global centers …

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 …

A global center for a vector field in the plane is a singular point p having R 2 filled of periodic
orbits with the exception of the singular point p. Polynomial differential systems of degree 2 …

A quadratic polynomial differential system can be identified with a single point of R12
through the coefficients. Using the algebraic invariant theory we classify all the quadratic …

1. Introduction and statements of the main results Page 1 NILPOTENT GLOBAL CENTERS OF
LINEAR SYSTEMS WITH CUBIC HOMOGENEOUS NONLINEARITIES JOHANNA D …

One of the classical and difficult problems in the theory of planar differential systems is to
classify their centers. Here we classify the global phase portraits in the Poincaré disk of the …

In this work we classify, with respect to the geometric equivalence relation, the global
configurations of singularities, finite and infinite, of quadratic differential systems possessing …