1996•Journal of Physics A Mathematical and GeneralOpen access

On the master symmetries related to certain classes of integrable Hamiltonian systems

Roman G. Smirnov

Abstract

We present the complete classification of master symmetries related to a non-degenerate Hamiltonian system that is integrable in the Arnol'd - Liouville's sense. It is shown that a -integrable Hamiltonian system cannot have generators of degree greater than 2. Specific properties of the master symmetries classified in terms of the action - angle variables are investigated.

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Key concepts: Integrable system, Homogeneous space, Hamiltonian (control theory), Degenerate energy levels, Hamiltonian system, Mathematical physics, Mathematics, Pure mathematics