A unified approach to linear and nonlinear normal forms for Hamiltonian systems

We prove that in all but one case the normal form of a real or complex Hami ltonian matrix which is irreducible and appropriately normalized can be com puted by Lie series methods in formally the same manner as one computes the normal form of a nonlinear Hamiltonian function. Calculations are emphasiz ed; the methods are illustrated with detailed examples, and for the sake of completeness the exceptional case is also reviewed and illustrated. Altern ate methods are also discussed, along with detailed examples. (C) 1999 Acad emic Press.