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 …

The relation between limit cycles of planar differential systems and the inverse integrating
factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From …

We apply the averaging theory of first order for discontinuous differential systems to study
the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the …

In this paper we give, as far as we know, the first method to detect non-algebraic invariant
curves for polynomial planar vector fields. This approach is based on the existence of a …

Phase portraits of uniform isochronous quartic centers - ScienceDirect Skip to main contentSkip
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Integrability of the Tolman–Oppenheimer–Volkoff equation - ScienceDirect Skip to main
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The goal of this monograph is to answer the question, is it possible to solve the dynamics
problem inside the configuration space instead of the phase space? By introducing a proper …

In this paper we study the maximum number of limit cycles that can bifurcate from a focus
singular point p 0 of an analytic, autonomous differential system in the real plane under an …

We consider the class of polynomial differential equations ẋ= λx− y+ P n (x, y)+ P 2 n− 1 (x,
y), ẏ= x+ λy+ Q n (x, y)+ Q 2 n− 1 (x, y) with n≥ 2, where P i and Q i are homogeneous …

In this paper we find necessary and sufficient conditions in order that a planar quasi–
homogeneous polynomial differential system has a polynomial or a rational first integral. We …