摘要
文章研究完备稠序的线性序拓扑空间上连续自映射f的不稳定流形。首先证明了不动点P的不稳定流形与P的任意邻域V的交集,通过f有限次迭代之后,会包含P的不稳定流形。然后利用此结果证明了f^k在p_i(1≤i≤k)的不稳定流形被f映射的象集合为f^k在f(p_i)的不稳定流形(其中p_i为f的k-周期轨上的点)。
In this paper, the unstable manifold of a continuous self-mapping f on a completely densely ordered linear ordered topological space is discussed. First of all, it is proved that the intersection of the unstable manifold of a fixed point p and arbitrary neighborhood of point p, by the finite iteration of f, will contains the unstable manifold of point p. Then, by using of the above conclusion, the following result is obtained, f maps the unstable manifold of f^k at pi （1 ≤ i ≤ k） to the unstable manifold of f^k at f（pi ） （ pi is a point in periodic orbit with period k of f ）.
出处
《四川理工学院学报（自然科学版）》
CAS
2009年第4期32-34,共3页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
基金
国家自然科学基金资助(10671134)
关键词
线性序拓扑空间
不稳定流形
周期点
连续自映射
linear ordered topological space
unstable manifold
periodic point
continuous self-mapping
