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 …

In this paper we deal with nonlinear differential systems of the form x′(t)= k∑ i= 0 εiFi (t, x)+
εk+ 1R (t, x, ε), where Fi: R× D→ Rn for i= 0, 1,···, k, and R: R× D×(− ε0, ε0)→ Rn are …

There is a folklore about the equivalence between the Melnikov method and the averaging
method for studying the number of limit cycles, which are bifurcated from the period annulus …

A new result on averaging theory for a class of discontinuous planar differential systems with
applications Page 1 Rev. Mat. Iberoam. 33 (2017), no. 4, 1247–1265 doi 10.4171/rmi/970 c …

We study a class of discontinuous piecewise linear differential systems with two zones
separated by the straight line x= 0. In x> 0, we have a linear saddle with its equilibrium point …

In this paper we develop an arbitrary order Melnikov function to study limit cycles bifurcating
from a periodic submanifold for autonomous piecewise smooth differential systems in R n …

In this work we first provide sufficient conditions to assure the persistence of some zeros of
functions having the form $\begin {align*}\newcommand {\e}{\varepsilon}\newcommand …

In this paper, we study bifurcations of small-amplitude limit cycles of Liénard systems of the
form x˙= y− F (x), y˙=− g (x), where g (x) is a cubic polynomial, and F (x) is a smooth or …

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 …

The averaging theory for studying periodic orbits of smooth differential systems has a long
history. Whereas the averaging theory for piecewise smooth differential systems appeared …