第二类对称典型域上的经典力学

Classical Mechanics on the Classical Domain of Type Two

四类对称典型域均可以表示成形如G/K(G是经典李群,K是G的极大紧子群)的齐性空间.本文通过构造适当的辛形式,得到了第二类对称典型域上经典力学的运动方程,并具体给出了两例刘维尔完全可积哈密顿系统.本文的方法可以类似地用来讨论第三类和第四类对称典型域上的经典力学.

Each classical bounded symmetric domain is diffeomorphic to a homogeneous space G/K（G is a classical Lie group and K is a maximal compact subgroup of G）.By constructing a suitable symplectic form,we study the classical mechanics and obtain the equation of motion on the classical domain of type two in this paper.Moreover,we present two examples of Liouville completely integrable Hamiltonian systems.Similarly,our methods can be used to evaluate the classical mechanics on the classical domains of type three and type four.