My aim in these notes is to consider some of the topics which surround the Poincaré center-
focus problem for polynomial systems. That is, given a polynomial system x= P (x, y), y= Q (x …

Singular perturbation problems are of common occurrence in all branches of applied
mathematics and engineering. These problems are encountered in various fields such as …

We provide a recurrence formula for the coefficients of the powers of ε in the series
expansion of the solutions around ε= 0 of the perturbed first-order differential equations …

In this paper, we consider the system x˙= y (1+ x) 2− ϵ P (x, y), y˙=− x (1+ x) 2+ ϵ Q (x, y)
where P (x, y) and Q (x, y) are arbitrary quadratic polynomials. We study the maximum …

In this paper we study the limit cycles of the system x˙=-y (x+ a)(y+ b)+ εP (x, y), y˙= x (x+
a)(y+ b)+ εQ (x, y) for ε sufficiently small, where a, b∈ R⧹{0}, and P, Q are polynomials of …

In this paper we provide an arbitrary order averaging theory for higher dimensional periodic
analytic differential systems. This result extends and improves results on averaging theory of …

This paper deals with the limit cycles of a class of cubic Hamiltonian systems under
polynomial perturbations. We suppose that the corresponding Hamiltonian system which …

Consider the vector field x′=− yG (x, y), y′= xG (x, y), where the set of critical points {G (x,
y)= 0} is formed by K straight lines, not passing through the origin and parallel to one or two …

We study the zero-Hopf bifurcation of the third-order differential equations x^ ′ ′ ′+(a_ 1
x+ a_ 0) x^ ′ ′+(b_ 1 x+ b_ 0) x^ ′+ x^ 2= 0, x ″′+(a 1 x+ a 0) x ″+(b 1 x+ b 0) x′+ x …

We investigate a class of n-dimensional periodic differential equations with multiple small
parameters by averaging method, and obtain sufficient conditions for the existence of …