Rigorous estimates for the series expansions of Hamiltonian perturbation theory

  title={Rigorous estimates for the series expansions of Hamiltonian perturbation theory},
  author={A. Giorgilli and L. Galgani},
  journal={Celestial mechanics},
  • A. Giorgilli, L. Galgani
  • Published 1985
  • Mathematics
  • Celestial mechanics
  • In the present paper we prove a theorem giving rigorous estimates in the problem of bringing to normal form a nearly integrable Hamiltonian system, using methods of classical perturbation theory, i.e. series expansions in the “small parameter” ε. For any order of normalization, we give a lower bound ɛ*r for the convergence radius of the normalized Hamiltonian, and a greater bound for the remainder, i.e. the non normalized part of the Hamiltonian. As an application, we consider the case of… CONTINUE READING
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