The completely integrable Hamiltonian systems have been applied to physics and mechanics intensively. We generate a family of completely integrable Hamiltonian systems from some kinds of exact Poisson structures in R^...The completely integrable Hamiltonian systems have been applied to physics and mechanics intensively. We generate a family of completely integrable Hamiltonian systems from some kinds of exact Poisson structures in R^3 by the realization of the Poisson algebra. Moreover, we prove that there is a Poisson algebra which cannot be realized by an exact Poisson structure.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10231020, and the Shanghai Shuguang Plan under Grant No 03SG10.
文摘The completely integrable Hamiltonian systems have been applied to physics and mechanics intensively. We generate a family of completely integrable Hamiltonian systems from some kinds of exact Poisson structures in R^3 by the realization of the Poisson algebra. Moreover, we prove that there is a Poisson algebra which cannot be realized by an exact Poisson structure.
