Non-autonomous normal forms for Hamiltonian systems

A method for calculating normal forms for non-autonomous periodically pertu rbed Hamiltonian systems is developed. The solution for an autonomous Hamil tonian normal form is well known, and involves the solution of a homologica l equation on the vector space of homogeneous scalar polynomials. An algori thm is presented for generating an analogous non-autonomous homological equ ation using Lie transforms. Solution of this equation will generate a norma l form for the non-autonomous Hamiltonian. Although this equation is define d on an infinite-dimensional space, it is shown that the problem can be red uced to an equivalent one on a finite-dimensional space. A solution can the n be found in an analogous way to the solution for the autonomous problem. It is also shown that the normal form satisfies invariance properties. Fina lly, an example problem is presented to illustrate the solution technique.