The computation of period constants is a way to study isochronous center for polynomial
differential systems. In this article, a new method to compute period constants is given. The …

In this paper, we study the center-focus problem for a generalized cubic Kukles system with
a nilpotent singular point, which consists of a cubic system with an extra 4th-order term. A …

In this paper we classify the phase portraits in the Poincaré disc of the centers of the
generalized class of Kukles systems x ̇=− y, y ̇= x+ ax 3 y+ bxy 3, symmetric with respect …

For the polynomial differential system,, where is a homogeneous polynomial of degree there
are the following two conjectures raised in 1999.(1) Is it true that the previous system for has …

This book presents in an elementary way the recent significant developments in the
qualitative theory of planar dynamical systems. The subjects are covered as follows: the …

For the polynomial differential system x=− y, y= x+ Qn (x, y), where Qn (x, y) is a
homogeneous polynomial of degree n there are the following two conjectures done in …

The problem of distinguishing whether a critical point of an analytic planar vector field with
pure imaginary eigenvalues is a center or a focus was already solved by Lyapunov by …

In this paper, we consider the limit cycles of a class of polynomial differential systems of the
form x=− y, y= x− f (x)− g (x) y− h (x) y2− l (x) y3, where f (x)= ϵf1 (x)+ ϵ2f2 (x), g (x)= ϵg1 …

We classify the global phase portraits in the Poincaré disc of the generalized Kukles systems
x ̇=− y, y ̇= x+ axy 6+ bx 3 y 4+ cx 5 y 2+ dx 7, which are symmetric with respect to both …

In the last years many papers giving different methods to compute the Poincaré–Liapunov
constants have been published. In (Appl. Math. Warsaw 28 (2002) 17) a new method to …