中文摘要：

基于拓扑分析,将标准李萨如图形的两个分运动方式由简谐函数推广到半波对称函数,得到了一类与标准李萨如图形拓扑等价,但更一般的周期平面曲线。构造出了与正弦函数拓扑等价的半波对称连续函数,给出了完成上述方案的具体程序。用科学计算软件Mathematica得到了由各种不同的幂函数生成的广义的李萨如图形,并给出了它们的统一规律。最后讨论了广义李萨如图形的对称性,给出了相应的判别条件。

英文摘要：

Based on the topological method,the standard Lissajous＇ figures generated by the simple harmonic functions was extend to a series of new results generated by the half wave symmetric functions,and the extended Lissajous＇ figures are equivalent to the standard ones in the topological properties. In addition,a class of new Lissajous＇ figures generated by the power functions using the Mathematica was obtained,and an unite law for them was given. At last,the symmetry of extended Lissajous＇ figures was discussed,and the corresponding discriminant conditions was given.