Resumen de Integrability and Linearizability of Three Dimensional Vector Fields

Waleed Aziz

• This paper deals with the integrability and linearizability problem of three dimensional systems x˙ = x(1 + ax + by + cz), y˙ = −y + dx2 + exy + f xz + gyz + hy2 + kz2, z˙ = z(1 + x + my + pz).

  More precisely, we give a complete set of necessary conditions for integrability and linearizability and then prove their sufficiency using Darboux method and Darboux inverse Jacobi multiplier, power series argument and a solution of a Riccati equation.