Normal form analysis of integrable Hamiltonian systems

Abstract

Normal form transformations are used to analyse two integrable cases of the generalized Hénon-Heiles Hamiltonian. The purpose of this Letter is to explore the explicit construction of transformations which give rise to the correct second integral for non-trivial integrable systems. For both investigated cases it is found that just one such transformation exists and that it cannot be constructed without the previous knowledge of the second integral.