有界的平面五次多项式系统  

Bounded polynomial systems of degree 5 in the plane

作　　者：杨小京[1] 

机构地区：[1]清华大学应用数学系

出　　处：《清华大学学报（自然科学版）》1998年第2期88-90,共3页Journal of Tsinghua University(Science and Technology)

摘　　要：平面多项式系统在动力系统理论研究中起着极重要的作用，目前很多问题需探索。文中从定性角度对平面五次多项式系统在无穷远赤道上只有孤立奇点时的有界性问题进行了讨论，并给出其所有可能的在无穷远点附近的相图，同时补充Ａ．Ｃｉｍａ和Ｊ．Ｌｌｉｂｒｅ一文中所遗漏的一个相图。A classification of plane bounded polynomial systems of degree 5 according to their phase portraits near equator is given. 59 different phase portraits of above systems are derived, the last 18 of them are the phase portraits of bounded polynomial systems of degree 3, 4 of them are that of degree 1.

关 键 词：多项式系统 相图 赤道 

分 类 号：O175.14[理学—数学]