Application Of Generalized Hopf Maps In Constructing Intergrable Hamiltonian Systems

In this paper, the application of generalized Hopf maps in constructing intergrable Hamilton systems is discussed. With the help of a Lie group homomorphism of SU(2) into SO(3), the Hopf map and two generalized Hopf maps are derived. Using corresponding Hopf maps, based on the Lie-Poisson structures, the reduction of three kinds of Poisson structures on C2 Nare discussed. It is proved that the resulting Poisson structures, which are obtained through the reduction procedure, are the same Lie-Poisson structure.