This review paper contains a brief summary of topics and concepts related with some open
problems of planar differential systems. Most of them are related with 16th Hilbert problem …

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 …

In this paper we consider perturbations of quasi-homogeneous planar Hamiltonian systems,
where the Hamiltonian function does not contain multiple factors. It is important to note that …

The center problem for degenerate singular points of planar systems (the degenerate-center
problem) is a poorly-understood problem in the qualitative theory of ordinary differential …

In this work we study the centers of planar analytic vector fields which are limit of linear type
centers. It is proved that all the nilpotent centers are limit of linear type centers and …

We give a new and short proof of the characterization of monodromic nilpotent critical points.
We also calculate the first generalized Lyapunov constants in order to solve the stability …

Generating limit cycles from a nilpotent critical point via normal forms Page 1 J. Math. Anal. Appl.
318 (2006) 271–287 www.elsevier.com/locate/jmaa Generating limit cycles from a nilpotent …

Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields -
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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 …

We prove that all the nilpotent centers of planar analytic differential systems are limit of
centers with purely imaginary eigenvalues, and consequently the Poincaré–Liapunov …