Y 空间连续自映射的伪轨跟踪性

Shadowing Property of Continuous Maps in Y Space

摘要: 伪轨跟踪性研究的是一个系统中任意扰动系统的轨道(即该系统的轨道)是否存在真正轨道使得在时间同步的意义下该轨道与伪轨的单步误差在指定范围内。它与系统的稳定性有着密切的联系，在动力系统的定性理论中起着重要的作用。本文扩展Gedeon和Kuchta的结论给出了Y 空间的连续自映射具有伪轨跟踪性的充分必要条件。

Abstract: The shadowing property study that whether or not arbitrary orbits of perturbation system (i.e. pseudo orbits of this system) exist actual orbits, which satisfy that error of single step between them is within the designated scope in the time synchronization. It has a close connection with the stability of a system, and plays a significant role in the qualitative theory of dynamical systems. This paper extends conclusion of Gedeon and Kuchta to prove the necessary and sufficient condition of the shadowing property of continuous maps in Y space into itself.