超椭园积分与五次系统

Hyperelliptic Integrals and The Quintic Differential System

本文研究在高压输电网的设计中出现的一类五次系统首先,在参数空间内对自治的Hamilton系统给出了当参数变化时(2)_(ε=0)的各种相图;其次利用超椭园积分给出了有界闭轨的参数方程;接着讨论了围绕原点的闭轨道族周期的单调性;最后研究了扰动系统(2)_ε的次谐波分枝和走向浑沌的条件。

The quintic system which describes the dynamics in the high——tension network was discussed. Various phases poraits were given to autonomous Hamiltonian system in the different regions of parameter space and calculate parameter equations of close orbits. The monotonicity of the period functions of some families of periodic solutions in the system had been inverstignted. The heteroclinicand subharmomic bifurcations and the chaotis dynamic behavior of the periodic disturbed system had been studied by using Melnikov method.