紧度量空间上轨道的分类和极限集有向同伦不变性

Classification of Orbit and Directed Homotopy of Limit Sets Invariance on the Compact Metric Space

本文利用正半轨道的ω极限集对紧度量空间的正半轨道进行分类,并讨论不动点和周期点的存在性.最后,引入轨道的正半同伦和负半同伦的概念,证明ω极限集和ω极限集在正半同伦和负半同伦的条件下是不变的,从而导出不动点和周期点在正半同伦和负半同伦的条件下保持不变.

This paper,classified positive semi-orbit of the compact metric space by ω-limit sets of positive semi-orbit,and discussed the existence of the fixed point and periodic point.Finally,introduced the concept of orbit positive semi-homotopy and negative semi-homotopy,and proved ω-limit sets and α-limit sets were unchanged under the condition of orbit positive semi-homotopy and negative semi-homotopy,and derived the fixed point and periodic point were unchanged.