Computation of normal forms of Hamiltonian systems in the presence of Poisson commuting integrals
Normal forms are an important tool in the analysis of Hamiltonian systems. The article discusses their construction for systems with symmetries. The authors describe explicitly how the Hamiltonian vector field and the symmetry generators can simultaneously be brought to normal form, based on the works of \textit{G. Cicogna} and \textit{G. Gaeta} [J. Phys. A 27, 461-476 (1994; Zbl 0822.34037); ibid. A 27, 7115-7124 (1994; Zbl 0847.58065)]. Parts of the algorithm have been implemented in the computer algebra system Maple. As a concrete application a Liouville integrable Hénon-Heiles system is treated in detail.
scientific article; zbMATH DE number 1382968