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 …

In this work we deal with analytic families of real planar vector fields $\mathcal {X} _\lambda
$ having a monodromic singularity at the origin for any $\lambda\in\Lambda\subset\mathbb …

In this work we study polynomial differential systems in the plane and define a new type of
integrability that we call Puiseux integrability. As its name indicates, the Puiseux integrability …

The general structure of irreducible invariant algebraic curves for a polynomial dynamical
system in C 2 is found. Necessary conditions for existence of exponential factors related to …

In this work we consider a family of cubic, with respect to the first derivative, second-order
ordinary differential equations. We study linearizability conditions for this family of equations …

A novel algebraic method for finding invariant algebraic curves for a polynomial vector field
in C 2 is introduced. The structure of irreducible invariant algebraic curves for Liénard …

In this paper, the short memory principle (SMP) is applied for solving the Abel differential
equation with fractional order. We evaluate the approximate solution at the end of required …

We consider the family of polynomial differential systems x'= x+(αy-βx)(αx2-bxy+ αy2) n, y'= y-
(βy+ αx)(αx2-bxy+ αy2) n, where α, b, ɑ, β are real constants and n is positive integer. We …

A concept of algebraic invariants and algebraically invariant solutions for autonomous
ordinary differential equations and systems of autonomous ordinary differential equations is …

The integrability problem consists of finding the class of functions a first integral of a given
planar polynomial differential system must belong to. We recall the characterization of …