Hamiltonian Systems with Widely Separated Frequencies

  title={Hamiltonian Systems with Widely Separated Frequencies},
  author={J. M. Tuwankotta and Ferdinand Verhulst},
In this paper we study two degree of freedom Hamiltonian systems and applications to nonlinear wave equations. Near the origin, we assume that near the linearized system has purely imaginary eigenvalues: i! 1 and i! 2 , with 0 < ! 2 =! 1 1 or ! 2 =! 1 1, which is interpreted as a perturbation of a problem with double zero eigenvalues. Using the averaging method, we compute the normal form and show that the dynamics diiers from the usual one for Hamiltonian systems at higher order resonances… CONTINUE READING