For asymptotically periodic systems, a powerful (phase) reduction of the dynamics is
obtained by computing the so-called isochrons, ie the sets of points that converge toward the …

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 paper, we study complex isochronous center problem for cubic complex planar vector
fields, which are assumed to be Z 2-equivariant with two symmetric centers. Such integrable …

In this paper, we investigate the linearizability problem for the two-dimensional planar
complex system. The necessary and sufficient conditions for the linearizability of this system …

In this paper we investigate the linearizability problem for the two-dimensional Lotka–
Volterra complex quartic systems which are linear systems perturbed by fourth degree …

We use Darboux polynomials to obtain an inverse integrating factor and present a method
for determining commuting transversal systems for a planar ordinary differential system. We …

We consider two-dimensional autonomous systems of differential equations where λ is a
real constant and P and Q are smooth functions of order greater than or equal to two. These …

Consider a family of planar systems x˙= X (x, ε) having a center at the origin and assume that
for ε= 0 they have an isochronous center. Firstly, we give an explicit formula for the first order …

In this paper, we consider complex smooth and analytic vector fields X in a neighborhood of
a nondegenerate singular point. It is proved the equivalence between linearizability and …

We propose a generalization of the notion of isochronicity for real polynomial autonomous
systems to the case of complex two dimensional systems of ODEs. We study the generalized …