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Centers of quasi-homogeneous polynomial planar systems
A. Algaba, N. Fuentes, C. García
In this paper we determine the centers of quasi-homogeneous polynomial planar vector fields of degree 0, 1, 2, 3 and 4. In addition, in every case we make a study of the reversibil…
Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system
A Algaba, N Fuentes, E Gamero +1
We consider a class of three-dimensional systems having an equilibrium point at the origin, whose principal part is of the form (-Dy h(x, y), Dx h(x,y), f(x,y))^T . This principal…
Non-formally integrable centers admitting an algebraic inverse integrating factor
A. Algaba, N. Fuentes, C. Garcia +1
Westudy the existence of a class of inverse integrating factor for a family of non formally integrable systems, in general, whose lowest-degree quasi-homogeneous term is a Hamilton…
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…