基于广义Hamilton系统的流定义的变换是保结构变换的性质,利用相应的Lie变换公式,获得了广义Hamilton系统的Hamilton函数的规范型及保结构变换的产生函数表达式。为阐明已获得这些理论结果的应用,具体研究了一类具有Lie-Poisson结构U(1,1)的三维广义Hamilton系统,明确计算了它的二阶规范型及其保结构变换的生成函数。
Based on the fact that the transformation of variables defined by the flow of generalized Hamiltonian system(GHS) was structure-preserving, through the related formula of Lie transformation , normal forms for a GHS and the generating function of corresponding transformation were derived .In order to illustrate the appli-cation of the obtained results , a class of three-dimensional GHS with U(1,1) Lie-Poisson structure was inves-tigated, its two-order normal form and the generating function of corresponding transformation were calculated explicitly .