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

José E. Mansilla

• 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.