Integrability and Linearizability of Three Dimensional Vector Fields

• Waleed Aziz ^[1]
  1. [1] Salahaddin University-Erbil

     Salahaddin University-Erbil

     Irak

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 13, Nº 2, 2014, págs. 197-213
• Idioma: inglés
• DOI: 10.1007/s12346-014-0113-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.