The Existence of Periodic Orbits to a Higher Dimensional Autonomous System with aNon-hyperbolic Singular Point *

具非双曲型奇点高维自治系统周期轨道的存在性(英文)

By means of theory of topological degree in nonlinear functional analysiscombining with qualitative analysis in ordinary differential equations, we discuss theexistence of nontrivial periodic orbits to a higher dimensional autonomous system witha non-hyperbolic singular point.

本文利用非线性泛函分析拓扑度理论与常微分方程定性分析相结合的方法讨论了奇点为非双曲型时高维自治系统周期轨道的存在性，得到了系统存在非常数周期轨道的充分条件．