Computation of normal forms of Hamiltonian systems in the presence of Poisson commuting integrals |
| |
Authors: | Jilali Mikram Fouad Zinoun |
| |
Institution: | (1) Département de Mathématiques et Informatique, Faculté des Sciences, Université de Rabat, BP 1014, Rabat, Morocco |
| |
Abstract: | The aim of this paper is to show the role of first integrals in further reducing the normal form unfolding of Hamiltonian
systems. Based on a work by Cicogna and Gaeta, the joint normal form approach for Hamiltonian vector fields is considered.
This normal form procedure, couched in a Lie-Poincaré scheme, allows us to see that we can reduce simultaneously the Hamiltonian
together with its Poisson commuting integrals to a simplified normal form - a joint normal form - which is given a simple
characterization. In this algorithmic procedure, approximate first integrals can be constructed (and used to simplify the
normal form) at the same time that we bring the Hamiltonian to normal form. Further, following Walcher, we show that we can
derive the joint normal form via a structure preserving transformation (in a sense to be specified). The approach is discussed
from an implementational standpoint and illustrated by a Liouville-integrable Hénon-Heiles system.
This revised version was published online in June 2006 with corrections to the Cover Date. |
| |
Keywords: | joint normal form Hamiltonian vector fields first integrals computer algebra |
本文献已被 SpringerLink 等数据库收录! |
|