The Lie Transformation in Hamiltonian Dynamics: A perturbation approach to Hamiltonian Chaos

Prof. Yutaka Abe, Hokkaido Automotive Engineering College, Sapporo.

Friday July 15th, 2005 at 3:30pm in K9509.


The Lie transformation is a perturbation method for Hamiltonian systems.
The idea of this method is to produce a near-identiy canonical transformation 
which simplifies the Hamiltonian. Lie transforms do not perturb the vector 
field itself, which consists of 2n scalar functions in a system of n degrees
of freedom, but rather, perturb the Hamiltonian, a single scalar function.
In the method of Lie transforms, we are concerned with generating a change 
of coordinates which will simplify the Hamiltonian.
As examples, the undamped Duffing equation and Henon-Heeiles system are
investigated to a certain extent with this method.
In this note, we will reveal the characteristic features of this 
perturbation method and its limitation for Hamitonian chaotic dynamics.