3 papers
math.DS2019
On the Integrability Problem for the Hopf-Zero singularity and its relation with the inverse Jacobi multiplier
A. Algaba, N. Fuentes, E. Gamero +1
In this paper we use the orbital normal form of the nondegenerate Hopf-zero singularity to obtain necessary conditions for the existence of first integrals for such singularity. Al…
math.DS2018
The analytic integrability problem for perturbations of homogeneous quadratic Lotka-Volterra systems
Antonio Algaba, Cristóbal García, Manuel Reyes
We solve the analytic integrability problem for diferential systems in the plane whose origin is an isolated singularity and the first homogeneous component is a quadratic Lotka-Vo…
math.DS2018
Analytic integrability around a nilpotent singularity
Antonio Algaba, Cristobal Garcia, Jaume Gine
In this work it is solved the analytic integrability problem around a nilpotent singularity of a differential system in the plane under generic conditions.