La forma normal de Lie en un caso crítico de un sistema hamiltoniano con tres grados de libertad y tres frecuencias iguales

• Mansilla, José ^[1]
  1. [1] Universidad de Magallanes

     Universidad de Magallanes

     Punta Arenas, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 23, Nº. 1, 2004, págs. 1-13
• Idioma: español
• DOI: 10.4067/S0716-09172004000100001
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• Resumen

  • In this work, we consider a Hamiltonian system with three degrees of freedom, whose linear part has all its roots pure imaginary and its three frequencies equal. We determine the kernel of the Lie operator and the normal form, according to Meyer of Hamiltonian in the diagonalizable case and in one of the nondiagonalizable cases, obtaining a normal form of the type obtained by Sokolskii and Mansilla in previous works.

• Referencias bibliográficas
  • Citas [1] Arnold V. I. : Mathematical Methods of Classical Machanics. SpringerVerlag New York, Inc., (1978).Forma normal de Lie 13
  • [2] Laub, A. J. and Meyer, K.: Canonical Forms for Symplectic and Hamiltonian Matrices. Celestial Mechanics, Vol. 9, pp. 233-238, (1974).
  • [3] Mansilla, J. E.: Sobre el núcleo del operador de Lie en el caso de tres grados de libertad y raíces imaginarias puras con dos frecuencias...
  • [4] Meyer, K. R. and Hall, G.R.: Introduction to Hamiltonian Dynamical System and the N-Body Problem. Springer-Verlag, New York, (1992).
  • [5] Sokolskii, A. G.: On the stability of autonomous Hamiltonian system with two degrees of freedom in the case equal frequencies. P. M. M.,...