动力系统的Poisson结构和可积变形

Poisson structures and integrable deformations of dynamical systems

利用动力系统的守恒积分构造Poisson结构,将动力系统表示为广义Hamilton系统的形式,并以一个三维动力系统为例,通过添加任意可微函数推广守恒积分,构造系统的可积变形,并给出变形后系统的Poisson结构,由此得到了新的刘维尔可积系统.

Poisson structures and integrable deformations of a three-dimensional dynamical system are studied in this paper.The first integrals of the given dynamical system are used to construct Poisson structures,then the system can be recast into the generalized Hamiltonian system.In addition,the integrable deformations of the initial system are constructed by adding arbitrary differentiable functions to the first integrals and the Poisson structures of the deformation systems are given.Thus new Liouville integrable systems are obtained.