柱面上一类动力系统非零伦闭轨的存在性与唯一性

On the Existence and Uniqueness of Closed Orbits Not Nullhomotopic for a Class of Dynamic Systems on the Cylinder

本文研究了柱面上一类比Liénard系统更为广泛的动力系统非零伦闭轨的存在性,唯一性及不存在性问题,获得了保证此系统非零伦闭轨存在,唯一及不存在的若干充分条件和在一定条件下存在唯一的一个充要条件.

In this paper we investigate the closed orbits not nullhomotopic for a class of dynamic systems on the cylinder. Some sufficient conditions, necessary and sufficient conditions for the existence and uniqueness or non-existence of closed orbits of this kind are obtained.