力学系统运动的类属性质研究

Study on Generic Properties of Dynamical Systems

动力系统类属性质研究着眼于对某一类系统的运动概括出来的共性.已知经典可积系统的运动是规则的,可用解析函数来描述,而不可积系统则相反.从简谐振子入手,指出动力对称性群的存在是能有规则运动的前提,还把这一概括出来的抽象陈述推广到了更一般的经典情形.量子力学是在哈密顿力学基础上,注入微观系统的特殊要求而建立起来的,所以这一关于经典规则运动的陈述可以推广到相应的量子情形。

ly outlined statement is then extended to more general classical cases. Quantum mechanics is established by imposing the particular requirements of microsystems to Hamiltonian mechanics. Hence, this statement for classical regular motion is able to be further extended to corresponding quantum cases such that the quantum-classical correspondence is more clearly clarified.