This paper studies the differential equation $\dot z= f (z) $, where $ f $ is an analytic function
in $\mathbb C $ except, possibly, at isolated singularities. We give a unify treatment of well …

In this paper we study the dynamics of real four-dimensional polynomial differential
equations of the forms q ̇= aqkqm or q ̇= qkaqm⁠, where q, a are quaternions, q is the …

This paper classifies the global structure of monic and centred one-variable complex
polynomial vector fields. The classification is achieved by means of combinatorial and …

In this paper, we are concerned with determining lower bounds of the number of limit cycles
for piecewise polynomial holomorphic systems with a straight line of discontinuity. We …

We tackle the problem of understanding the geometry and dynamics of singular complex
analytic vector fields $ X $ with essential singularities on a Riemann surface $ M $(compact …

In this paper we aim to find the highest number of critical periods in a class of planar systems
of polynomial differential equations for fixed degree having a center. We fix our attention to …

We study the center problem for planar systems with a linear center at the origin that in
complex coordinates have a nonlinearity formed by the sum of two monomials. Our first …

Let z˙= f (z) be an holomorphic differential equation having a center at p, and consider the
following perturbation z˙= f (z)+ εR (z, z¯). We give an integral expression, similar to an …

In this work we focus on the configuration (location and stability) of simple critical points of
polynomial differential equations of the form ż= f (z), z∈ C. The case where all the critical …

In this paper, we introduce geometric tools to study the families of rational vector fields of a
given degree over ℂ ℙ 1 CP^1. To a generic vector field of such a parametric family, we …